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A261612
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Expansion of Product_{k>=0} (1 + x^(3*k+1)).
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23
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1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 3, 3, 2, 4, 4, 2, 4, 5, 3, 5, 7, 4, 5, 8, 6, 7, 10, 7, 7, 12, 10, 9, 14, 12, 10, 16, 16, 13, 19, 19, 15, 22, 24, 19, 25, 28, 22, 29, 35, 28, 33, 40, 33, 38, 48, 41, 44, 55, 48, 51, 66, 59, 58, 74, 69
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OFFSET
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0,12
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
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FORMULA
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a(n) ~ exp(Pi*sqrt(n)/3) / (2^(4/3) * sqrt(3) * n^(3/4)) * (1 - (Pi/144 + 9/(8*Pi)) / sqrt(n)). - Vaclav Kotesovec, Aug 26 2015, extended Jan 16 2017
G.f.: Sum_{k>=0} x^(k*(3*k - 1)/2) / Product_{j=1..k} (1 - x^(3*j)). - Ilya Gutkovskiy, Nov 24 2020
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Product[(1 + x^(3*k+1)), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 1; Do[If[Mod[k, 3] == 1, Do[poly[[j + 1]] += poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly (* Vaclav Kotesovec, Jan 13 2017 *)
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CROSSREFS
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Cf. A000009, A000700, A035382, A169975.
Cf. A015128, A080054, A261610, A261611, A262928.
Sequence in context: A067594 A089533 A284312 * A184241 A054390 A161068
Adjacent sequences: A261609 A261610 A261611 * A261613 A261614 A261615
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KEYWORD
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nonn
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AUTHOR
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Vaclav Kotesovec, Aug 26 2015
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STATUS
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approved
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