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 A109706 Number of partitions of n into parts each equal to 4 mod 7. 4
 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 3, 2, 1, 4, 3, 2, 2, 5, 3, 2, 4, 6, 3, 3, 6, 6, 3, 6, 7, 6, 4, 9, 8, 6, 7, 11, 8, 7, 11, 12, 8, 11, 14, 13, 9, 16, 16, 13, 13, 21, 17, 14, 20, 24, 18, 19, 26, 26, 19, 27, 31, 27, 24, 36, 34, 29, 34, 43 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,23 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: 1/product(1-x^(4+7j), j=0..infinity). - Emeric Deutsch, Apr 14 2006 a(n) ~ Gamma(4/7) * exp(Pi*sqrt(2*n/21)) / (2^(25/14) * 3^(2/7) * 7^(3/14) * Pi^(3/7) * n^(11/14)) * (1 + (23*Pi/(168*sqrt(42)) - 11*sqrt(6/7)/(7*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017 a(n) = (1/n)*Sum_{k=1..n} A284445(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 28 2017 EXAMPLE a(22)=2 because we have 22=18+4=11+11. MAPLE g:=1/product(1-x^(4+7*j), j=0..20): gser:=series(g, x=0, 93): seq(coeff(gser, x, n), n=0..90); # Emeric Deutsch, Apr 14 2006 MATHEMATICA nmax=100; CoefficientList[Series[Product[1/(1-x^(7*k+4)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 27 2015 *) CROSSREFS Sequence in context: A335225 A070106 A182595 * A174541 A029444 A122191 Adjacent sequences: A109703 A109704 A109705 * A109707 A109708 A109709 KEYWORD nonn AUTHOR Erich Friedman, Aug 07 2005 EXTENSIONS Changed offset to 0 and added a(0)=1 by Vaclav Kotesovec, Feb 27 2015 STATUS approved

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Last modified December 6 01:58 EST 2023. Contains 367594 sequences. (Running on oeis4.)