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A153649
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A row sum 7^n triangular recursion sequence:Prime[j]=7=scale; A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (j+1)*Prime[j]*A(n - 2, k - 1).
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0
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2, 7, 7, 2, 94, 2, 2, 341, 341, 2, 2, 413, 3972, 413, 2, 2, 485, 16320, 16320, 485, 2, 2, 557, 31260, 171660, 31260, 557, 2, 2, 629, 48792, 774120, 774120, 48792, 629, 2, 2, 701, 68916, 1917012, 7556340, 1917012, 68916, 701, 2, 2, 773, 91632, 3693648
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Row sums are:
{2, 14, 98, 686, 4802, 33614, 235298, 1647086, 11529602, 80707214,...}.
Plot of the lowest level of the fractal is:
a = Table[Table[If[m <= n, If[Mod[A[n, m], 7] == 0, 0, 1], 0], {m, 1, 10}], {n, 1, 10}] ;
ListDensityPlot[a, Mesh -> False, Axes -> False]
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FORMULA
| A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (j+1)*Prime[j]*A(n - 2, k - 1).
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EXAMPLE
| {2},
{7, 7},
{2, 94, 2},
{2, 341, 341, 2},
{2, 413, 3972, 413, 2},
{2, 485, 16320, 16320, 485, 2},
{2, 557, 31260, 171660, 31260, 557, 2},
{2, 629, 48792, 774120, 774120, 48792, 629, 2},
{2, 701, 68916, 1917012, 7556340, 1917012, 68916, 701, 2},
{2, 773, 91632, 3693648, 36567552, 36567552, 3693648, 91632, 773, 2}
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MATHEMATICA
| Clear[t, n, m, A, a]; j = 3;
A[2, 1] := A[2, 2] = Prime[j];
A[3, 2] = 2*Prime[j]^2 - 4;
A[4, 2] = A[4, 3] = Prime[j]^3 - 2;
A[n_, 1] := 2; A[n_, n_] := 2;
A[n_, k_] := A[n - 1, k - 1] + A[n - 1, k] + (j+1)*Prime[j]*A[n - 2, k - 1];
Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}] ;
Flatten[%] Table[Sum[A[n, m], {m, 1, n}], {n, 1, 10}] ;
Table[Sum[A[n, m], {m, 1, n}]/(2*Prime[j]^(n - 1)), {n, 1, 10}]
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CROSSREFS
| Sequence in context: A016639 A138341 A153520 * A020770 A177003 A164767
Adjacent sequences: A153646 A153647 A153648 * A153650 A153651 A153652
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 30 2008
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