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A263401
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Expansion of Product_{k>=1} (1 + x^k - x^(2*k)).
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13
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1, 1, 0, 2, 0, 1, 3, 1, 1, 2, 6, 1, 4, 2, 5, 10, 5, 4, 9, 7, 8, 21, 9, 13, 13, 19, 13, 27, 32, 23, 29, 33, 27, 45, 37, 45, 79, 49, 57, 68, 82, 67, 101, 83, 109, 155, 124, 113, 174, 148, 171, 196, 215, 198, 262, 310, 269, 330, 314, 342, 414, 430, 393, 536, 493
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) ~ sqrt(log(phi)) * phi^sqrt(8*n) / (2^(3/4)*sqrt(Pi)*n^(3/4)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jan 03 2016
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MATHEMATICA
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nmax = 80; CoefficientList[Series[Product[1+x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; p = ConstantArray[0, nmax + 1]; p[[1]] = 1; p[[2]] = 1; p[[3]] = -1; Do[Do[p[[j+1]] = p[[j+1]] + p[[j - k + 1]] - If[j < 2*k, 0, p[[j - 2*k + 1]]], {j, nmax, k, -1}]; , {k, 2, nmax}]; p (* Vaclav Kotesovec, May 10 2018 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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