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A153654 A row sum 23^n triangular recursion sequence:Prime[j]=23=scale; A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (2*j+1)*Prime[j]*A(n - 2, k - 1). 0
2, 23, 23, 2, 1054, 2, 2, 12165, 12165, 2, 2, 13041, 484928, 13041, 2, 2, 13917, 5814074, 5814074, 13917, 2, 2, 14793, 11526908, 223541684, 11526908, 14793, 2, 2, 15669, 17623430, 2775818930, 2775818930, 17623430, 15669, 2, 2, 16545, 24103640 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are:

{2, 46, 1058, 24334, 511014, 11655986, 246625090, 5586916062, 118948996454,

2679380312002,...}.

Plot of the lowest level of the fractal is:

a = Table[Table[If[m <= n, If[Mod[A[n, m], 23] == 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..39.

FORMULA

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

EXAMPLE

{2},

{23, 23},

{2, 1054, 2},

{2, 12165, 12165, 2},

{2, 13041, 484928, 13041, 2},

{2, 13917, 5814074, 5814074, 13917, 2},

{2, 14793, 11526908, 223541684, 11526908, 14793, 2},

{2, 15669, 17623430, 2775818930, 2775818930, 17623430, 15669, 2},

{2, 16545, 24103640, 7830701156, 103239353768, 7830701156, 24103640, 16545, 2},

{2, 17421, 30967538, 15556243706, 1324102927334, 1324102927334, 15556243706, 30967538, 17421, 2}

MATHEMATICA

Clear[t, n, m, A, a]; j = 9;

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] + (2*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}]

CROSSREFS

Sequence in context: A104644 A158992 A128365 * A153656 A242037 A233692

Adjacent sequences:  A153651 A153652 A153653 * A153655 A153656 A153657

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 30 2008

STATUS

approved

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Last modified May 23 03:10 EDT 2019. Contains 323507 sequences. (Running on oeis4.)