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A153637
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A triangular sequence with row sums (3^(n - 1)*(n + 1)!) starting at n=1 which was calculated by steps.
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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]
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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.
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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}
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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}];
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CROSSREFS
| Sequence in context: A201899 A201894 A023400 * A137618 A021338 A021889
Adjacent sequences: A153634 A153635 A153636 * A153638 A153639 A153640
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com) and Gary Adamson, Dec 29 2008, Jan 01 2009
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