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Search: id:A153650
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| A153650 |
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A row sum 11^n triangular recursion sequence:Prime[j]=11=scale; A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (j+4)*Prime[j]*A(n - 2, k - 1). |
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| 2, 11, 11, 2, 238, 2, 2, 1329, 1329, 2, 2, 1529, 26220, 1529, 2, 2, 1729, 159320, 159320, 1729, 2, 2, 1929, 312420, 2914420, 312420, 1929, 2, 2, 2129, 485520, 18999520, 18999520, 485520, 2129, 2, 2, 2329, 678620, 50414620, 326526620, 50414620
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:
{2, 22, 242, 2662, 29282, 322102, 3543122, 38974342, 428717762, 4715895382,...}.
Plot of the lowest level of the fractal is:
a = Table[Table[If[m <= n, If[Mod[A[n, m], 11] == 0, 0, 1], 0], {m, 1, 10}], {n, 1, 10}] ;
ListDensityPlot[a, Mesh -> False, Axes -> False]
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FORMULA
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A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (j+4)*Prime[j]*A(n - 2, k - 1).
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EXAMPLE
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{2},
{11, 11},
{2, 238, 2},
{2, 1329, 1329, 2},
{2, 1529, 26220, 1529, 2},
{2, 1729, 159320, 159320, 1729, 2},
{2, 1929, 312420, 2914420, 312420, 1929, 2},
{2, 2129, 485520, 18999520, 18999520, 485520, 2129, 2},
{2, 2329, 678620, 50414620, 326526620, 50414620, 678620, 2329, 2},
{2, 2529, 891720, 99159720, 2257893720, 2257893720, 99159720, 891720, 2529, 2}
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MATHEMATICA
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Clear[t, n, m, A, a]; j = 5;
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+4)*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
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Sequence in context: A064743 A109868 A153521 this_sequence A086862 A027828 A106371
Adjacent sequences: A153647 A153648 A153649 this_sequence A153651 A153652 A153653
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 30 2008
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