A153637 A triangular sequence with row sums (3^(n - 1)*(n + 1)!) starting at n=1 which was calculated by steps.

2, 9, 9, 2, 212, 2, 2, 1618, 1618, 2, 2, 2100, 54116, 2100, 2, 2, 2786, 609572, 609572, 2786, 2, 2, 3712, 1582558, 26220736, 1582558, 3712, 2, 2, 4914, 3257870, 393546494, 393546494, 3257870, 4914, 2, 2, 6428, 6069056, 1593218212, 20609969404

Offset

1,1

Comments

Row sums are 3^(n - 1)*(n + 1)!.

A fractal plot is:

a0 = Table[Table[If[m <= n, If[Mod[A[n, m], 3] == 0, 0, 1], 0], {m, 1, 12}], {n, 1, 12}];

ListDensityPlot[a0, Mesh -> False, Axes -> False]

Links

Table of n, a(n) for n=1..41.

Formula

A(n,k)=A(n - 1, k - 1) + A(n - 1, k) + b[n]*n*(n + 1)*A(n - 2, k - 1);

b[n] is an array function of n.

Example

{2},
{9, 9},
{2, 212, 2},
{2, 1618, 1618, 2},
{2, 2100, 54116, 2100, 2},
{2, 2786, 609572, 609572, 2786, 2},
{2, 3712, 1582558, 26220736, 1582558, 3712, 2},
{2, 4914, 3257870, 393546494, 393546494, 3257870, 4914, 2},
{2, 6428, 6069056, 1593218212, 20609969404, 1593218212, 6069056, 6428, 2},
{2, 8290, 10645504, 4629106368, 388201427036, 388201427036, 4629106368, 10645504, 8290, 2},
{2, 10536, 17866010, 11449232704, 2180421367268, 23900788525360, 2180421367268, 11449232704, 17866010, 10536, 2}

Mathematica

Clear[a]; a = {{2}, {9, 9}, {2, 212, 2}, {2, 1618, 1618, 2},
{2, 2100, 54116, 2100, 2}, {2, 2786, 609572, 609572, 2786, 2},
{2, 3712, 1582558, 26220736, 1582558, 3712, 2}, {2, 4914, 3257870, 393546494, 393546494, 3257870, 4914, 2},
{2, 6428, 6069056, 1593218212, 20609969404, 1593218212, 6069056, 6428, 2},
{2, 8290, 10645504, 4629106368, 388201427036, 388201427036, 4629106368, 10645504, 8290, 2},
{2, 10536, 17866010, 11449232704, 2180421367268, 23900788525360, 2180421367268, 11449232704, 17866010, 10536, 2}};
Flatten[a] Table[Apply[Plus, a[[n]]], {n, 1, Length[a]}];
Table[Apply[Plus, a[[n]]]/(3^(n - 1)*(n + 1)!), {n, 1, Length[a]}];
Clear[A, b]; Table[b[n] = (39 n + 9 n^2)/(n + 1), {n, 1, 4}];
b[5] = 8; b[6] = 57/7; b[7] = 33/4; b[8] = 25/3; b[9] = 42/5;
b[10] = 93/11; b[11] = 17/2; b[12] = 111/13;
A[2, 1] := A[2, 2] = 9; A[3, 2] = 212;
A[4, 2] = 1618; A[4, 3] = 1618;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + b[n]*n*(n + 1)*A[n - 2, k - 1];
a = Table[A[n, k], {n, 12}, {k, n}];
Flatten[a]
Table[Apply[Plus, a[[n]]], {n, 1, 12}];
Table[Apply[Plus, a[[n]]]/(3^(n - 1)*(n + 1)!), {n, 1, 12}];

Crossrefs

Sequence in context: A201899 A201894 A023400 * A137618 A340866 A021338

Adjacent sequences: A153634 A153635 A153636 * A153638 A153639 A153640

Keyword

nonn,uned,tabl

Author

Roger L. Bagula and Gary W. Adamson, Dec 29 2008, Jan 01 2009

Status

approved