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A153651 A row sum 13^n triangular recursion sequence:Prime[j]=13=scale; A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (j+6)*Prime[j]*A(n - 2, k - 1). 0
2, 13, 13, 2, 334, 2, 2, 2195, 2195, 2, 2, 2483, 52152, 2483, 2, 2, 2771, 368520, 368520, 2771, 2, 2, 3059, 726360, 8194776, 726360, 3059, 2, 2, 3347, 1125672, 61619496, 61619496, 1125672, 3347, 2, 2, 3635, 1566456, 166614648, 1295091960, 166614648 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are:

{2, 26, 338, 4394, 57122, 742586, 9653618, 125497034, 1631461442, 21208998746,...}.

Plot of the lowest level of the fractal is:

a = Table[Table[If[m <= n, If[Mod[A[n, m], 13] == 0, 0, 1], 0], {m, 1, 10}], {n, 1, 10}] ;

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

LINKS

Table of n, a(n) for n=1..42.

FORMULA

A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (j+5)*Prime[j]*A(n - 2, k - 1).

EXAMPLE

{2},

{13, 13},

{2, 334, 2},

{2, 2195, 2195, 2},

{2, 2483, 52152, 2483, 2},

{2, 2771, 368520, 368520, 2771, 2},

{2, 3059, 726360, 8194776, 726360, 3059, 2},

{2, 3347, 1125672, 61619496, 61619496, 1125672, 3347, 2},

{2, 3635, 1566456, 166614648, 1295091960, 166614648, 1566456, 3635, 2},

{2, 3923, 2048712, 329152200, 10273294536, 10273294536, 329152200, 2048712, 3923, 2}

MATHEMATICA

Clear[t, n, m, A, a]; j = 6;

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+5)*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}]

CROSSREFS

Sequence in context: A002591 A037055 A065584 * A229908 A320339 A075032

Adjacent sequences:  A153648 A153649 A153650 * A153652 A153653 A153654

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 30 2008

STATUS

approved

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Last modified January 25 07:41 EST 2020. Contains 331241 sequences. (Running on oeis4.)