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A035384
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Number of partitions of n into parts 6k+2 or 6k+3.
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0
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1, 0, 1, 1, 1, 1, 2, 1, 3, 3, 3, 4, 5, 4, 7, 7, 8, 10, 12, 11, 16, 16, 18, 22, 25, 25, 33, 34, 38, 45, 50, 52, 65, 67, 75, 87, 95, 101, 121, 126, 141, 160, 174, 187, 218, 229, 254, 285, 308, 333, 380, 401, 443, 492, 530, 574, 646, 683, 752, 828, 890, 964, 1072, 1137, 1246
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OFFSET
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0,7
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LINKS
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Table of n, a(n) for n=0..64.
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FORMULA
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Euler transform of period 6 sequence [ 0, 1, 1, 0, 0, 0, ...]. - Michael Somos, Feb 09 2012
G.f.: 1 / (Product_{k>0} (1 - x^(6*k - 4)) * (1 - x^(6*k - 3))). - Michael Somos, Feb 09 2012
a(n) ~ exp(Pi*sqrt(2*n)/3) * Gamma(1/3) / (4 * 2^(1/3) * sqrt(3) * Pi^(2/3) * n^(2/3)). - Vaclav Kotesovec, Aug 27 2015
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Product[1/((1 - x^(6k+2))*(1 - x^(6k+3))), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 27 2015 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, polcoeff( 1 / prod( k=1, (n+4)\6, (1 - x^(6*k - 4)) * (1 - x^(6*k - 3)), 1 + x * O(x^n)), n))} /* Michael Somos, Feb 09 2012 */
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CROSSREFS
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Sequence in context: A174257 A105637 A029161 * A360033 A303974 A153868
Adjacent sequences: A035381 A035382 A035383 * A035385 A035386 A035387
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KEYWORD
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nonn
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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