Triangular numbers: Difference between revisions

=={{header|FreeBASIC}}==

{{trans|Wren}}

<syntaxhighlight lang="freebasic">Dim As Integer n, r, t(0 To 30)

t(0) = 0

Print "The first 30 triangular numbers are:"

For n = 1 To 30

t(n) = t(n-1) + n - 1

If n Mod 6 = 0 Then Print Using "####"; t(n) Else Print Using "####"; t(n);

Next n

Print !"\nThe first 30 tetrahedral numbers are:"

For n = 1 To 30

t(n) += t(n-1)

Print Using "#####"; t(n);

If n Mod 6 = 0 Then Print

Next n

Print !"\nThe first 30 pentatopic numbers are:"

For n = 1 To 30

t(n) += t(n-1)

Print Using "######"; t(n);

If n Mod 6 = 0 Then Print

Next n

Print !"\nThe first 30 12-simplex numbers are:"

For r = 5 To 12

For n = 1 To 30

t(n) += t(n-1)

If r = 12 Then

Print Using "###########"; t(n);

If n Mod 6 = 0 Then Print

End If

Next n

Next r

#define cRec27 1/sqr(27)

Dim As Integer xs(1 To 4) = {7140, 21408696, 26728085384, 14545501785001}

Dim As Double x, y, z

For i As Byte = 1 To 4

z = xs(i)

Print !"\nRoots of"; xs(i); ":"

Print " triangular:"; (Sqr(8*z+1)-1)/2

y = 3*z

x = Sqr((y-cRec27)*(y+cRec27))

Print "tetrahedral:"; Iif(x < y, Exp(Log(y+x)/3)+Exp(Log(y-x)/3)-1, Exp(Log(6)/3)*Exp(Log(z)/3)-1)

Print " pentatopic:"; (Sqr(5+4*Sqr(24*z+1))-3)/2

Next i

Sleep</syntaxhighlight>

{{out}}

<pre>The first 30 triangular numbers are:

0 1 3 6 10 15

21 28 36 45 55 66

78 91 105 120 136 153

171 190 210 231 253 276

300 325 351 378 406 435

The first 30 tetrahedral numbers are:

0 1 4 10 20 35

56 84 120 165 220 286

364 455 560 680 816 969

1140 1330 1540 1771 2024 2300

2600 2925 3276 3654 4060 4495

The first 30 pentatopic numbers are:

0 1 5 15 35 70

126 210 330 495 715 1001

1365 1820 2380 3060 3876 4845

5985 7315 8855 10626 12650 14950

17550 20475 23751 27405 31465 35960

The first 30 12-simplex numbers are:

0 1 13 91 455 1820

6188 18564 50388 125970 293930 646646

1352078 2704156 5200300 9657700 17383860 30421755

51895935 86493225 141120525 225792840 354817320 548354040

834451800 1251677700 1852482996 2707475148 3910797436 5586853480

Roots of 7140:

triangular: 119

tetrahedral: 34.00000000179027

pentatopic: 18.87664661592801

Roots of 21408696:

triangular: 6543

tetrahedral: 503.5611663345483

pentatopic: 149.0609473752659

Roots of 26728085384:

triangular: 231205.4055652559

tetrahedral: 5431.99993864654

pentatopic: 893.4424567516849

Roots of 14545501785001:

triangular: 5393607.158145173

tetrahedral: 44355.77737655847

pentatopic: 4321</pre>