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A153280
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Eigensequence of triangle A153279
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2
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1, 3, 15, 165, 4785, 397155, 97302975, 71128474725, 155700231173025, 1021860617188563075, 20115326249356864131375, 1187830130350772183821825125, 210422919761508941591852499068625, 111827787746815596446398867662527275875
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OFFSET
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0,2
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LINKS
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FORMULA
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Given triangle A153279, let a new triangle = M shifted down one row, inserting a "1" in (0,0). Triangle equals lim_{n->oo} M^n.
a(n) ~ c * 3^(n*(n-1)/2), where c = QPochhammer(-2, 1/3) = 6.80914656805984199... - Vaclav Kotesovec, Jan 22 2023
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EXAMPLE
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Triangle M =
1;
1;
2, 1;
4, 2, 3;
8, 4, 6, 9;
16, 8, 12, 18, 27;
...
M^n rapidly converges to this sequence with sufficiently large n.
a(0) = 1, a(1) = 1*(2+3^0) = 3, a(2) = 3*(2+3^1) = 15, a(3) = 15*(2+3^2) = 165, a(4) = 165*(2+3^3) = 4785, ... - Philippe Deléham, Sep 27 2014
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MATHEMATICA
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RecurrenceTable[{a[n+1] == a[n]*(2 + 3^n), a[0] == 1}, a, {n, 0, 15}] (* Vaclav Kotesovec, Jan 22 2023 *)
Table[2^n * QPochhammer[-1/2, 3, n], {n, 0, 15}] (* Vaclav Kotesovec, Jan 22 2023 *)
nxt[{n_, a_}]:={n+1, a(2+3^n)}; NestList[nxt, {0, 1}, 20][[;; , 2]] (* Harvey P. Dale, Mar 28 2024 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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