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Sudan function

Sudan function
You are encouraged to solve this task according to the task description, using any language you may know.

The Sudan function is a classic example of a recursive function, notable especially because it is not a primitive recursive function. This is also true of the better-known Ackermann function. The Sudan function was the first function having this property to be published.

The Sudan function is usually defined as follows (svg):

  <big>
:$\begin{array}{lll} F_0 (x, y) & = x+y \\ F_{n+1} (x, 0) & = x & \text{if } n \ge 0 \\ F_{n+1} (x, y+1) & = F_n (F_{n+1} (x, y), F_{n+1} (x, y) + y + 1) & \text{if } n\ge 0 \\ \end{array}$
</big>


Write a function which returns the value of F(x, y).

Translation of: Javascript
with Ada.Text_IO; use Ada.Text_IO; procedure Sudan_Function is    function F (N, X, Y : Natural) return Natural   is (if    N = 0 then X + Y       elsif Y = 0 then X       else  F (N => N - 1,                X => F (N, X, Y - 1),                Y => F (N, X, Y - 1) + Y)); begin   Put_Line ("F0 (0, 0) = " & F (0, 0, 0)'Image);   Put_Line ("F1 (1, 1) = " & F (1, 1, 1)'Image);   Put_Line ("F1 (3, 3) = " & F (1, 3, 3)'Image);   Put_Line ("F2 (1, 1) = " & F (2, 1, 1)'Image);   Put_Line ("F2 (2, 1) = " & F (2, 2, 1)'Image);   Put_Line ("F3 (1, 1) = " & F (3, 1, 1)'Image);end Sudan_Function;
Output:
F0 (0, 0) =  0
F1 (1, 1) =  3
F1 (3, 3) =  35
F2 (1, 1) =  8
F2 (2, 1) =  27
F3 (1, 1) =  10228


ALGOL 68

Translation of: Wren

...with a minor optimisation.

BEGIN # compute some values of the Sudan function                          #    PROC sudan = ( INT n, x, y )INT:         IF   n = 0 THEN x + y         ELIF y = 0 THEN x         ELSE             INT s = sudan( n, x, y - 1 );             sudan( n - 1, s, s + y )         FI # sudan # ;    FOR n FROM 0 TO 1 DO        print( ( "Values of F(", whole( n, 0 ), ", x, y):", newline ) );        print( ( "y/x    0   1   2   3   4   5",            newline ) );        print( ( "----------------------------",            newline ) );        FOR y FROM 0 TO 6 DO            print( ( whole( y, 0 ), "  |" ) );            FOR x FROM 0 TO 5 DO                print( ( whole( sudan( n, x, y ), -4 ) ) )            OD;            print( ( newline ) )        OD;        print( ( newline ) )    OD;    print( ( newline ) );    print( ( "F(2, 1, 1) = ", whole( sudan( 2, 1, 1 ), 0 ), newline ) );    print( ( "F(3, 1, 1) = ", whole( sudan( 3, 1, 1 ), 0 ), newline ) );    print( ( "F(2, 2, 1) = ", whole( sudan( 2, 2, 1 ), 0 ), newline ) )END
Output:
Values of F(0, x, y):
y/x    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   2   3   4   5   6
2  |   2   3   4   5   6   7
3  |   3   4   5   6   7   8
4  |   4   5   6   7   8   9
5  |   5   6   7   8   9  10
6  |   6   7   8   9  10  11

Values of F(1, x, y):
y/x    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   3   5   7   9  11
2  |   4   8  12  16  20  24
3  |  11  19  27  35  43  51
4  |  26  42  58  74  90 106
5  |  57  89 121 153 185 217
6  | 120 184 248 312 376 440

F(2, 1, 1) = 8
F(3, 1, 1) = 10228
F(2, 2, 1) = 27


AWK

 # syntax: GAWK -f SUDAN_FUNCTION.AWKBEGIN {    for (n=0; n<=1; n++) {      printf("sudan(%d,x,y)\n",n)      printf("y/x    0   1   2   3   4   5\n")      printf("%s\n",strdup("-",28))      for (y=0; y<=6; y++) {        printf("%2d | ",y)        for (x=0; x<=5; x++) {          printf("%3d ",sudan(n,x,y))        }        printf("\n")      }      printf("\n")    }    n=1; x=3; y=3; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))    n=2; x=1; y=1; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))    n=2; x=2; y=1; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))    n=3; x=1; y=1; printf("sudan(%d,%d,%d)=%d\n",n,x,y,sudan(n,x,y))    exit(0)}function sudan(n,x,y) {    if (n == 0) { return(x+y) }    if (y == 0) { return(x) }    return sudan(n-1, sudan(n,x,y-1), sudan(n,x,y-1)+y)}function strdup(str,n,  i,new_str) {    for (i=1; i<=n; i++) {      new_str = new_str str    }    return(new_str)}
Output:
sudan(0,x,y)
y/x    0   1   2   3   4   5
----------------------------
0 |   0   1   2   3   4   5
1 |   1   2   3   4   5   6
2 |   2   3   4   5   6   7
3 |   3   4   5   6   7   8
4 |   4   5   6   7   8   9
5 |   5   6   7   8   9  10
6 |   6   7   8   9  10  11

sudan(1,x,y)
y/x    0   1   2   3   4   5
----------------------------
0 |   0   1   2   3   4   5
1 |   1   3   5   7   9  11
2 |   4   8  12  16  20  24
3 |  11  19  27  35  43  51
4 |  26  42  58  74  90 106
5 |  57  89 121 153 185 217
6 | 120 184 248 312 376 440

sudan(1,3,3)=35
sudan(2,1,1)=8
sudan(2,2,1)=27
sudan(3,1,1)=10228


BASIC

BASIC256

Translation of: FreeBASIC
for n = 0 to 1    print "Values of F(" & n & ", x, y):"    print "y/x    0   1   2   3   4   5"    print ("-"*28)    for y = 0 to 6        print y; "  |";        for x = 0 to 5            print rjust(string(F(n,x,y)),4);        next x        print    next y    printnext n print "F(2,1,1) = "; F(2,1,1)print "F(3,1,1) = "; F(3,1,1)print "F(2,2,1) = "; F(2,2,1)end function F(n, x, y)    if n = 0 then return x + y    if y = 0 then return x    return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)end function
Output:
Same as FreeBASIC entry.

Procedure.d F(n.i, x.i, y.i)  If n = 0    ProcedureReturn x + y  ElseIf y = 0    ProcedureReturn x  Else     ProcedureReturn F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)  EndIfEndProcedure OpenConsole()For n = 0 To 1  PrintN("Values of F(" + Str(n) + ", x, y):")  PrintN("y/x     0       1       2       3       4       5")  PrintN("---------------------------------------------------")  For y = 0 To 6    Print(Str(y) + " |")    For x = 0 To 5      Print(#TAB$+ F(n,x,y)) Next x PrintN("") Next y PrintN("")Next n PrintN("F(2,1,1) = " + Str(F(2,1,1)))PrintN("F(3,1,1) = " + Str(F(3,1,1)))PrintN("F(2,2,1) = " + Str(F(2,2,1)))Input()CloseConsole() Output: Similat to FreeBASIC entry. Yabasic Translation of: FreeBASIC for n = 0 to 1 print "Values of F(", n, ", x, y):" print "y/x 0 1 2 3 4 5" print "----------------------------" for y = 0 to 6 print y, " | "; for x = 0 to 5 print F(n,x,y) using ("###"); next x print next y printnext n print "F(2,1,1) = ", F(2,1,1)print "F(3,1,1) = ", F(3,1,1)print "F(2,2,1) = ", F(2,2,1)end sub F(n, x, y) if n = 0 return x + y if y = 0 return x return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)end sub Output: Same as FreeBASIC entry. C Translation of: Javascript  //Aamrun, 11th July 2022 #include <stdio.h> int F(int n,int x,int y) { if (n == 0) { return x + y; } else if (y == 0) { return x; } return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);} int main() { printf("F1(3,3) = %d",F(1,3,3)); return 0;}  Output F1(3,3) = 35  C++ Translation of: C  //Aamrun , 11th July, 2022 #include <iostream>using namespace std; int F(int n,int x,int y) { if (n == 0) { return x + y; } else if (y == 0) { return x; } return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);} int main() { cout << "F(1,3,3) = "<<F(1,3,3)<<endl; return 0;}  Output F(1,3,3) = 35  C# Translation of: C  //Aamrun, 11th July 2022 using System; namespace Sudan{ class Sudan { static int F(int n,int x,int y) { if (n == 0) { return x + y; } else if (y == 0) { return x; } return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y); } static void Main(string[] args) { Console.WriteLine("F(1,3,3) = " + F(1,3,3)); } }}  Output F(1,3,3) = 35  Factor Works with: Factor version 0.99 2022-04-03 USING: combinators kernel math prettyprint ; : sudan ( n x y -- z ) { { [ pick zero? ] [ nipd + ] } { [ dup zero? ] [ drop nip ] } [ [ 2drop 1 - ] [ 1 - sudan dup ] [ 2nip + sudan ] 3tri ] } cond ; 3 1 1 sudan . Output: 10228  Or with locals: USING: combinators kernel locals math prettyprint ; :: sudan ( n x y -- z ) { { [ n zero? ] [ x y + ] } { [ y zero? ] [ x ] } [ n 1 - n x y 1 - sudan dup y + sudan ] } cond ; FreeBASIC Translation of: Wren and Phyton Function F(n As Integer, x As Integer, y As Integer) As Integer If n = 0 Then Return x + y If y = 0 Then Return x Return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y)End Function Dim As Integer n, x, yFor n = 0 To 1 Print " Values of F(" & n & ", x, y):" Print " y/x 0 1 2 3 4 5" Print String(29, "-") For y = 0 To 6 Print y; " |"; For x = 0 To 5 Print Using "####"; F(n,x,y); Next x Print Next y PrintNext n Print "F(2,1,1) ="; F(2,1,1)Print "F(3,1,1) ="; F(3,1,1)Print "F(2,2,1) ="; F(2,2,1)Sleep Output: Same as Wren entry. Go Translation of: Wren package main import "fmt" func F(n, x, y int) int { if n == 0 { return x + y } if y == 0 { return x } return F(n-1, F(n, x, y-1), F(n, x, y-1)+y)} func main() { for n := 0; n < 2; n++ { fmt.Printf("Values of F(%d, x, y):\n", n) fmt.Println("y/x 0 1 2 3 4 5") fmt.Println("----------------------------") for y := 0; y < 7; y++ { fmt.Printf("%d |", y) for x := 0; x < 6; x++ { fmt.Printf("%4d", F(n, x, y)) } fmt.Println() } fmt.Println() } fmt.Printf("F(2, 1, 1) = %d\n", F(2, 1, 1)) fmt.Printf("F(3, 1, 1) = %d\n", F(3, 1, 1)) fmt.Printf("F(2, 2, 1) = %d\n", F(2, 2, 1))} Output: Identical to Wren example.  Haskell import Control.Monad.Memo (Memo, memo, startEvalMemo)import Data.List.Split (chunksOf)import System.Environment (getArgs)import Text.Tabular (Header(..), Properties(..), Table(..))import Text.Tabular.AsciiArt (render) type SudanArgs = (Int, Integer, Integer) -- Given argument (n, x, y) calculate Fₙ(x, y). For performance reasons we do-- the calculation in a memoization monad.sudan :: SudanArgs -> Memo SudanArgs Integer Integersudan (0, x, y) = return$ x + ysudan (_, x, 0) = return xsudan (n, x, y) = memo sudan (n, x, y-1) >>= \x2 -> sudan (n-1, x2, x2 + y) -- A table of Fₙ(x, y) values, where the rows are y values and the columns are-- x values.sudanTable :: Int -> [Integer] -> [Integer] -> StringsudanTable n xs ys = render show show show                   $Table (Group NoLine$ map Header ys)                           (Group NoLine $map Header xs)$ chunksOf (length xs)                   $startEvalMemo$ sequence                   $[sudan (n, x, y) | y <- ys, x <- xs] main :: IO ()main = do args <- getArgs case args of [n, xlo, xhi, ylo, yhi] -> do putStrLn$ "Fₙ(x, y), where the rows are y values " ++                 "and the columns are x values.\n"      putStr $sudanTable (read n) [read xlo .. read xhi] [read ylo .. read yhi] _ -> error "Usage: sudan n xmin xmax ymin ymax" Output: $ sudan 0 0 5 0 6
Fₙ(x, y), where the rows are y values and the columns are x values.

+---++---------------+
|   || 0 1 2 3  4  5 |
+===++===============+
| 0 || 0 1 2 3  4  5 |
| 1 || 1 2 3 4  5  6 |
| 2 || 2 3 4 5  6  7 |
| 3 || 3 4 5 6  7  8 |
| 4 || 4 5 6 7  8  9 |
| 5 || 5 6 7 8  9 10 |
| 6 || 6 7 8 9 10 11 |
+---++---------------+

J

Translation of: Javascript

This is, of course, not particularly efficient and some results are too large for a computer to represent.

F=: {{ 'N X Y'=. y assert. N>:0  if. 0=N do. X+Y  elseif. Y=0 do. X  else. F (N-1),(F N,X,Y-1), Y+F N, X, Y-1  end.}}"1
Examples:
   F 0 0 00   F 1 1 13   F 2 1 18   F 3 1 110228   F 2 2 127

Java

Translation of: C
 //Aamrun, 11th July 2022 public class Main {   private static int F(int n,int x,int y) {  	if (n == 0) {    	return x + y;  	}  	 else if (y == 0) {    	return x;  	}   	return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y); }   public static void main(String[] args) {    System.out.println("F(1,3,3) = " + F(1,3,3));  }}

Output

F(1,3,3) = 35


JavaScript

 /** * @param {bigint} n * @param {bigint} x * @param {bigint} y * @returns {bigint} */function F(n, x, y) {  if (n === 0) {    return x + y;  }   if (y === 0) {    return x;  }   return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y);}

using Memoize @memoize function sudan(n, x, y)   return n == 0 ? x + y : y == 0 ? x : sudan(n - 1, sudan(n, x, y - 1), sudan(n, x, y - 1) + y)end foreach(t -> println("sudan($(t[1]),$(t[2]), $(t[3])) = ", sudan(t[1], t[2], t[3])), ((0,0,0), (1,1,1), (2,1,1), (3,1,1), (2,2,1)))  Output: sudan(0, 0, 0) = 0 sudan(1, 1, 1) = 3 sudan(2, 1, 1) = 8 sudan(3, 1, 1) = 10228 sudan(2, 2, 1) = 27  Perl Three ways of doing the same thing. use v5.36;use experimental 'for_list'; sub F1($n, $x,$y) { $n ?$y ? F1($n-1, F2($n,$x,$y-1), F3($n,$x,$y-1)+$y) : $x :$x+$y } sub F2($n, $x,$y) { $n == 0 ?$x+$y :$y == 0 ? $x : F2($n-1, F1($n,$x,$y-1), F3($n,$x,$y-1)+$y) } sub F3($n, $x,$y) {  return $x +$y if $n == 0; return$x      if $y == 0; F3($n-1, F1($n,$x, $y-1), F2($n, $x,$y-1) + $y)} for my($n,$x,$y) (0,0,0, 1,1,1, 2,1,1, 3,1,1, 2,2,1) {    say join ' ',F1($n,$x,$y), F2($n,$x,$y), F3($n,$x,$y)} Output: 0 0 0 3 3 3 8 8 8 10228 10228 10228 27 27 27 Phix with javascript_semantics function F(integer n, x, y) if n=0 then return x+y end if if y=0 then return x end if integer t = F(n,x,y-1) return F(n-1,t,t+y) end function for n=0 to 1 do printf(1,"Values of F(%d, x, y):\n",n) printf(1,"y/x 0 1 2 3 4 5\n") printf(1,"----------------------------\n") for y=0 to 6 do sequence r = apply(true,F,{n,tagset(5,0),y}) printf(1,"%d |%s\n",{y,join(r,"",fmt:="%4d")}) end for printf(1,"\n") end for for t in {{2,1,1},{3,1,1},{2,2,1}} do integer {n,x,y} = t printf(1,"F(%d, %d, %d) = %d\n",{n,x,y,F(n,x,y)}) end for  Output same as Wren. PHP Translation of: C  #Aamrun , 11th July 2022 <?phpfunction F(int$n,int $x,int$y) {  if ($n == 0) { return$x + $y; } else if ($y == 0) {    return $x; } return F($n - 1, F($n,$x, $y - 1), F($n, $x,$y - 1) + $y);}echo "F(1,3,3) = " . F(1,3,3); ?>  Output F(1,3,3) = 35  Python Translation of: Javascript  # Aamrun, 11th July 2022 def F(n,x,y): if n==0: return x + y elif y==0: return x else: return F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y) print("F(1,3,3) = ", F(1,3,3))  Output F(1,3,3) = 35  R Translation of: C  #Aamrun, 11th July 2022 F <- function(n, x, y) { if(n==0){ F <- x+y return (F) } else if(y == 0) { F <- x return (F) } F <- F(n - 1, F(n, x, y - 1), F(n, x, y - 1) + y) return (F)} print(paste("F(1,3,3) = " , F(1,3,3)))  Output [1] "F(1,3,3) = 35"  Raku Outputting wiki-tables to more closely emulate the wikipedia examples. Not very efficient but good enough. multi F (0,$x, $y) {$x + $y }multi F ($n where * > 0, $x, 0) {$x }multi F ($n,$x, $y) { F($n-1, F($n,$x, $y-1), F($n, $x,$y-1) + $y) } # Testingfor 0, 6, 1, 15 ->$f, $g { my @range = ^$g;    say "\{|class=\"wikitable\"\n", "|+ F\<sub>$f\</sub> (x,y)\n" ~ '!x\y!!', join '!!', @range; ->$r { say "|-\n" ~ '|' ~ join '||', $r, @range.map:{ F($f, $r,$_) } } for @range;    say( "|}" );}
Output:
F0 (x,y)
x\y 0 1 2 3 4 5
0 0 1 2 3 4 5
1 1 2 3 4 5 6
2 2 3 4 5 6 7
3 3 4 5 6 7 8
4 4 5 6 7 8 9
5 5 6 7 8 9 10
F1 (x,y)
x\y 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0 0 1 4 11 26 57 120 247 502 1013 2036 4083 8178 16369 32752
1 1 3 8 19 42 89 184 375 758 1525 3060 6131 12274 24561 49136
2 2 5 12 27 58 121 248 503 1014 2037 4084 8179 16370 32753 65520
3 3 7 16 35 74 153 312 631 1270 2549 5108 10227 20466 40945 81904
4 4 9 20 43 90 185 376 759 1526 3061 6132 12275 24562 49137 98288
5 5 11 24 51 106 217 440 887 1782 3573 7156 14323 28658 57329 114672
6 6 13 28 59 122 249 504 1015 2038 4085 8180 16371 32754 65521 131056
7 7 15 32 67 138 281 568 1143 2294 4597 9204 18419 36850 73713 147440
8 8 17 36 75 154 313 632 1271 2550 5109 10228 20467 40946 81905 163824
9 9 19 40 83 170 345 696 1399 2806 5621 11252 22515 45042 90097 180208
10 10 21 44 91 186 377 760 1527 3062 6133 12276 24563 49138 98289 196592
11 11 23 48 99 202 409 824 1655 3318 6645 13300 26611 53234 106481 212976
12 12 25 52 107 218 441 888 1783 3574 7157 14324 28659 57330 114673 229360
13 13 27 56 115 234 473 952 1911 3830 7669 15348 30707 61426 122865 245744
14 14 29 60 123 250 505 1016 2039 4086 8181 16372 32755 65522 131057 262128

Ruby

 def sudan(n, x, y)  return x + y if n == 0  return x if y == 0   sudan(n - 1, sudan(n, x, y - 1), sudan(n, x, y - 1) + y)end

Output

puts sudan(1, 3, 3)
> 35


Vlang

Translation of: Wren
fn sudan(n int, x int, y int) int {    if n == 0 {       return x + y    }    if y == 0 {        return x    }    return sudan(n-1, sudan(n, x, y-1), sudan(n, x, y-1) + y)} fn main() {    for n := 0; n < 2; n++ {        println("Values of F($n, x, y):") println("y/x 0 1 2 3 4 5") println("----------------------------") for y := 0; y < 7; y++ { print("$y  |")            for x := 0; x < 6; x++ {                s := sudan(n, x, y)                print("${s:4}") } println('') } println('') } println("F(2, 1, 1) =${sudan(2, 1, 1)}")    println("F(3, 1, 1) = ${sudan(3, 1, 1)}") println("F(2, 2, 1) =${sudan(2, 2, 1)}")}
Output:
Identical to Wren example.


Wren

Library: Wren-fmt
import "./fmt" for Fmt var F = Fn.new { |n, x, y|    if (n == 0) return x + y    if (y == 0) return x    return F.call(n - 1, F.call(n, x, y-1), F.call(n, x, y-1) + y)} for (n in 0..1) {    System.print("Values of F(%(n), x, y):")    System.print("y/x    0   1   2   3   4   5")    System.print("----------------------------")    for (y in 0..6) {        System.write("%(y)  |")        for (x in 0..5) {            var sudan = F.call(n, x, y)            Fmt.write("\$4d", sudan)        }        System.print()    }    System.print()}System.print("F(2, 1, 1) = %(F.call(2, 1, 1))")System.print("F(3, 1, 1) = %(F.call(3, 1, 1))")System.print("F(2, 2, 1) = %(F.call(2, 2, 1))")
Output:
Values of F(0, x, y):
y/x    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   2   3   4   5   6
2  |   2   3   4   5   6   7
3  |   3   4   5   6   7   8
4  |   4   5   6   7   8   9
5  |   5   6   7   8   9  10
6  |   6   7   8   9  10  11

Values of F(1, x, y):
y/x    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   3   5   7   9  11
2  |   4   8  12  16  20  24
3  |  11  19  27  35  43  51
4  |  26  42  58  74  90 106
5  |  57  89 121 153 185 217
6  | 120 184 248 312 376 440

F(2, 1, 1) = 8
F(3, 1, 1) = 10228
F(2, 2, 1) = 27


XPL0

Translation of: Wren
func F; int N, X, Y;[if N = 0 then return X + Y; if Y = 0 then return X;return F(N-1, F(N, X, Y-1), F(N, X, Y-1) + Y);]; int N, X, Y;[Format(4, 0);for N:= 0 to 1 do    [Text(0, "Values of F("); IntOut(0, N);  Text(0, ", X, Y):^m^j");     Text(0, "Y/X    0   1   2   3   4   5^m^j");     Text(0, "----------------------------^m^j");     for Y:= 0 to 6 do        [IntOut(0, Y);  Text(0, "  |");        for X:= 0 to 5 do            RlOut(0, float(F(N, X, Y)));        CrLf(0);        ];    CrLf(0);    ];Text(0, "F(2, 1, 1) = ");  IntOut(0, F(2, 1, 1));  CrLf(0);Text(0, "F(3, 1, 1) = ");  IntOut(0, F(3, 1, 1));  CrLf(0);Text(0, "F(2, 2, 1) = ");  IntOut(0, F(2, 2, 1));  CrLf(0);]
Output:
Values of F(0, X, Y):
Y/X    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   2   3   4   5   6
2  |   2   3   4   5   6   7
3  |   3   4   5   6   7   8
4  |   4   5   6   7   8   9
5  |   5   6   7   8   9  10
6  |   6   7   8   9  10  11

Values of F(1, X, Y):
Y/X    0   1   2   3   4   5
----------------------------
0  |   0   1   2   3   4   5
1  |   1   3   5   7   9  11
2  |   4   8  12  16  20  24
3  |  11  19  27  35  43  51
4  |  26  42  58  74  90 106
5  |  57  89 121 153 185 217
6  | 120 184 248 312 376 440

F(2, 1, 1) = 8
F(3, 1, 1) = 10228
F(2, 2, 1) = 27