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Fibonacci n-step number sequences: Difference between revisions

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Fibonacci n-step number sequences (view source)

Revision as of 21:16, 22 April 2024

6,456 bytes added ,  26 days ago
Added various BASIC dialects (Chipmunk Basic, QBasic, and QB64)
(→‎{{header|Vlang}}: Rename "Vlang" in "V (Vlang)")
(Added various BASIC dialects (Chipmunk Basic, QBasic, and QB64))
 
(9 intermediate revisions by 8 users not shown)
Line 758:
decanacci: 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172 …
Lucas: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364 …"</syntaxhighlight>
 
=={{header|Arturo}}==
<syntaxhighlight lang="arturo">naccis: #[
lucas: [2 1]
fibonacci: [1 1]
tribonacci: [1 1 2]
tetranacci: [1 1 2 4]
pentanacci: [1 1 2 4 8]
hexanacci: [1 1 2 4 8 16]
heptanacci: [1 1 2 4 8 16 32]
octonacci: [1 1 2 4 8 16 32 64]
nonanacci: [1 1 2 4 8 16 32 64 128]
decanacci: [1 1 2 4 8 16 32 64 128 256]
]
 
anyNacci: function [start, count][
n: size start
result: new start
do.times: count-n ->
result: result ++ sum last.n:n result
 
return join.with:", " to [:string] result
]
 
loop naccis [k,v][
print [pad (k ++ ":") 12 anyNacci v 15]
]</syntaxhighlight>
 
{{out}}
 
<pre> lucas: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843
fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
tribonacci: 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, 927, 1705, 3136
tetranacci: 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773, 1490, 2872, 5536
pentanacci: 1, 1, 2, 4, 8, 16, 31, 61, 120, 236, 464, 912, 1793, 3525, 6930
hexanacci: 1, 1, 2, 4, 8, 16, 32, 63, 125, 248, 492, 976, 1936, 3840, 7617
heptanacci: 1, 1, 2, 4, 8, 16, 32, 64, 127, 253, 504, 1004, 2000, 3984, 7936
octonacci: 1, 1, 2, 4, 8, 16, 32, 64, 128, 255, 509, 1016, 2028, 4048, 8080
nonanacci: 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2040, 4076, 8144
decanacci: 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, 8172</pre>
 
=={{header|AutoHotkey}}==
Line 838 ⟶ 878:
</pre>
 
=={{header|BASIC256BASIC}}==
==={{header|BASIC256}}===
<syntaxhighlight lang="basic256"># Rosetta Code problem: https://www.rosettacode.org/wiki/Fibonacci_n-step_number_sequences
# by Jjuanhdez, 06/2022
Line 901 ⟶ 942:
decanacci => 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2045, 4088, ...
lucas => 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, ...</pre>
 
==={{header|Chipmunk Basic}}===
{{trans|BASIC256}}
{{works with|Chipmunk Basic|3.6.4}}
<syntaxhighlight lang="vbnet">100 sub fib(a())
110 erase f
120 dim f(24)
130 b = 0
140 for x = 1 to ubound(a)
150 b = b+1
160 f(x) = a(x)
170 next x
180 for i = b to 12+b
190 print using "#### ";f(i-b+1);
200 for j = (i-b+1) to i
210 f(i+1) = f(i+1)+f(j)
220 next j
230 next i
240 print
250 end sub
260 cls
270 print " fibonacci =>";
280 dim a(2)
290 a(1) = 1 : a(2) = 1
300 fib(a())
310 print " tribonacci =>";
320 dim a(3)
330 a(1) = 1 : a(2) = 1 : a(3) = 2
340 fib(a())
350 print " tetranacci =>";
360 dim c(4)
370 c(1) = 1 : c(2) = 1 : c(3) = 2 : c(4) = 4
380 fib(c())
390 print " lucas =>";
400 dim d(2)
410 d(1) = 2 : d(2) = 1
420 fib(d())
430 end</syntaxhighlight>
 
==={{header|QBasic}}===
{{trans|BASIC256}}
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
{{works with|QB64}}
<syntaxhighlight lang="qbasic">DECLARE SUB fib (a() AS INTEGER)
 
CLS
PRINT " fibonacci =>";
DIM a(1 TO 2) AS INTEGER
a(1) = 1: a(2) = 1
CALL fib(a())
PRINT " tribonacci =>";
DIM b(1 TO 3) AS INTEGER
b(1) = 1: b(2) = 1: b(3) = 2
CALL fib(b())
PRINT " tetranacci =>";
DIM c(1 TO 4) AS INTEGER
c(1) = 1: c(2) = 1: c(3) = 2: c(4) = 4
CALL fib(c())
PRINT " lucas =>";
DIM d(1 TO 2) AS INTEGER
d(1) = 2: d(2) = 1
CALL fib(d())
END
 
SUB fib (a() AS INTEGER)
DIM f(24)
b = 0
FOR x = 1 TO UBOUND(a)
b = b + 1
f(x) = a(x)
NEXT x
FOR i = b TO 12 + b
PRINT USING "#### "; f(i - b + 1);
FOR j = (i - b + 1) TO i
f(i + 1) = f(i + 1) + f(j)
NEXT j
NEXT i
END SUB</syntaxhighlight>
 
==={{header|QB64}}===
{{trans|BASIC256}}
<syntaxhighlight lang="qbasic">Rem $Dynamic
 
Cls
Print " fibonacci =>";
Dim a(1 To 2) As Integer
a(1) = 1
a(2) = 1
Call fib(a())
Print " tribonacci =>";
ReDim _Preserve a(1 To 3)
a(3) = 2
Call fib(a())
Print " tetranacci =>";
ReDim _Preserve a(1 To 4)
a(4) = 4
Call fib(a())
Print " lucas =>";
ReDim a(1 To 2)
a(1) = 2
a(2) = 1
Call fib(a())
End
 
Sub fib (a() As Integer)
Dim f(24)
b = 0
For x = 1 To UBound(a)
b = b + 1
f(x) = a(x)
Next x
For i = b To 12 + b
Print Using "#### "; f(i - b + 1);
For j = (i - b + 1) To i
f(i + 1) = f(i + 1) + f(j)
Next j
Next i
End Sub</syntaxhighlight>
 
=={{header|Batch File}}==
Line 1,649 ⟶ 1,809:
=={{header|Delphi}}==
See [[#Pascal]].
=={{header|EasyLang}}==
<syntaxhighlight>
proc sequ n$ val[] n . .
write n$ & ": "
il = len val[]
len val[] n
for i = il + 1 to n
for j = 1 to il
val[i] += val[i - j]
.
.
for v in val[]
write v & " "
.
print ""
.
sequ "Fibonacci" [ 1 1 ] 10
sequ "Tribonacci" [ 1 1 2 ] 10
sequ "Tetrabonacci" [ 1 1 2 4 ] 10
sequ "Lucas" [ 2 1 ] 10
</syntaxhighlight>
{{out}}
<pre>
Fibonacci: 1 1 2 3 5 8 13 21 34 55
Tribonacci: 1 1 2 4 7 13 24 44 81 149
Tetrabonacci: 1 1 2 4 8 15 29 56 108 208
Lucas: 2 1 3 4 7 11 18 29 47 76
</pre>
 
=={{header|EchoLisp}}==
<syntaxhighlight lang="scheme">
Line 2,126 ⟶ 2,315:
=={{header|Fōrmulæ}}==
 
{{FormulaeEntry|page=https://formulae.org/?script=examples/Fibonacci_n-step_number_sequences}}
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation &mdash;i.e. XML, JSON&mdash; they are intended for storage and transfer purposes more than visualization and edition.
 
'''Solution'''
Programs in Fōrmulæ are created/edited online in its [https://formulae.org website], However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
 
According to the requirements, the program must generate a series, and the order (Fibonacci, Tribonacci, etc) should be determined according with the initial values.
In '''[https://formulae.org/?example=Fibonacci_n-step_number_sequences this]''' page you can see the program(s) related to this task and their results.
 
In this case, the number n indicates how many terms of the series will be generated.
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 01.png]]
 
The following generates a Fibonacci series of 15 terms:
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 02.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 03.png]]
 
The following generates a Lucas series of 15 terms:
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 04.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 05.png]]
 
The following generates a Tribonacci series of 15 terms:
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 06.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 07.png]]
 
'''Generating initial values.''' The initial values can be generated by the following function:
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 08.png]]
 
Note that it is a recursive function, and it calls the previously defined function. It requires the initial values as a seed: (1, 1) for Fibonacci style (Fibonacci, Tribonacci, etc), and (2, 1) for Lucas style.
 
The following generates the initial values for Fibonacci series.
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 09.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 10.png]]
 
The following generates the initial values for Lucas series.
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 11.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 12.png]]
 
'''Generating tables of series for Fibonacci and Lucas'''
 
This generates a tables of series for Fibonacci (15 terms), for orders 2 to 10 (Fibonacci, Tribonacci, etc.)
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 13.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 14.png]]
 
This generates a tables of series for Lucas (15 terms), for orders 2 to 15:
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 15.png]]
 
[[File:Fōrmulæ - Fibonacci n-step number sequences 16.png]]
 
=={{header|Go}}==
Line 2,230 ⟶ 2,473:
 
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import DataControl.ListMonad (tailszipWithM_)
import ControlData.MonadList (zipWithM_tails)
 
fiblike :: [Integer] -> [Integer]
fiblike st = xs where
where
xs = st ++ map (sum . take n) (tails xs)
xs = st <> map (sum . take n) (tails xs)
n = length st
n = length st
 
nstep :: Int -> [Integer]
nstep n = fiblike $ take n $ 1 : iterate (2 *) 1
 
main :: IO ()
main = do
mapM_ (print $. take 10 $. fiblike) [[1, 1], [2, 1]]
zipWithM_
print $ take 10 $ fiblike [2,1]
zipWithM_ ( \n name -> do putStr (name ++ "nacci -> ")
putStr (name <> "nacci -> ")
print $ take 15 $ nstep n)
print $ take 15 $ nstep n
[2..] (words "fibo tribo tetra penta hexa hepta octo nona deca")</syntaxhighlight>
)
[2 ..]
(words "fibo tribo tetra penta hexa hepta octo nona deca")</syntaxhighlight>
{{out}}
<pre>
Line 4,225 ⟶ 4,472:
Lucas:
2 1 3 4 7 11 18 29 47 76 123 199 ...
</pre>
 
=={{header|RPL}}==
≪ OVER SIZE → len n
≪ LIST→
<span style="color:red">1</span> + len '''FOR''' j
n DUPN
<span style="color:red">2</span> n '''START''' + '''NEXT'''
'''NEXT''' len →LIST
≫ ≫ ‘<span style="color:blue">NFIB</span>’ STO
 
<span style="color:red">{1 1} 15</span> <span style="color:blue">NFIB</span>
DUP <span style="color:red">1 3</span> SUB <span style="color:red">15</span> <span style="color:blue">NFIB</span>
DUP <span style="color:red">1 4</span> SUB <span style="color:red">15</span> <span style="color:blue">NFIB</span>
<span style="color:red">{2 1} 15</span> <span style="color:blue">NFIB</span>
{{out}}
<pre>
4: { 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 }
3: { 1 1 2 4 7 13 24 44 81 149 274 504 927 1705 3136 }
2: { 1 1 2 4 8 15 29 56 108 208 401 773 1490 2872 5536 }
1: { 2 1 3 4 7 11 18 29 47 76 123 199 322 521 843 }
</pre>
 
Line 4,495 ⟶ 4,763:
var len = xs.len
len >= k && break
xs << xs.ftslice(max(0, len - n)).sum
}
return xs
Line 4,871 ⟶ 5,139:
{{trans|Kotlin}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./fmt" for Fmt
 
var fibN = Fn.new { |initial, numTerms|
Jjuanhdez
2,122

edits

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