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 A153656 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+3)*Prime[j]*A(n - 2, k - 1). 0
 2, 23, 23, 2, 1054, 2, 2, 12165, 12165, 2, 2, 13133, 533412, 13133, 2, 2, 14101, 6422240, 6422240, 14101, 2, 2, 15069, 12779580, 270482476, 12779580, 15069, 2, 2, 16037, 19605432, 3385203976, 3385203976, 19605432, 16037, 2, 2, 17005, 26899796 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS First version was wrong: the j function increases with larger j. Row sums are: {2, 46, 1058, 24334, 559682, 12872686, 296071778, 6809650894, 156621970562, 3602305322926,...}. 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 FORMULA A(n,k)= A(n - 1, k - 1) + A(n - 1, k) + (2*j+3)*Prime[j]*A(n - 2, k - 1). EXAMPLE {2}, {23, 23}, {2, 1054, 2}, {2, 12165, 12165, 2}, {2, 13133, 533412, 13133, 2}, {2, 14101, 6422240, 6422240, 14101, 2}, {2, 15069, 12779580, 270482476, 12779580, 15069, 2}, {2, 16037, 19605432, 3385203976, 3385203976, 19605432, 16037, 2}, {2, 17005, 26899796, 9577346548, 137413443860, 9577346548, 26899796, 17005, 2}, {2, 17973, 34662672, 19073670000, 1782044310816, 1782044310816, 19073670000, 34662672, 17973, 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+3)*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: A158992 A128365 A153654 * A242037 A233692 A084323 Adjacent sequences:  A153653 A153654 A153655 * A153657 A153658 A153659 KEYWORD nonn,uned,tabl AUTHOR Roger L. Bagula, Dec 30 2008 STATUS approved

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Last modified May 24 00:38 EDT 2019. Contains 323528 sequences. (Running on oeis4.)