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 A103259 Number of partitions of 2n prime to 3,5 with all odd parts occurring with even multiplicities. There is no restriction on the even parts. 2
 1, 2, 4, 6, 10, 14, 20, 28, 40, 54, 72, 96, 126, 164, 212, 274, 350, 444, 560, 704, 878, 1092, 1352, 1668, 2048, 2506, 3056, 3714, 4500, 5436, 6552, 7872, 9436, 11280, 13456, 16012, 19014, 22532, 26648, 31452, 37052, 43572, 51148, 59940, 70128, 81922, 95548 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is also the sequence A103257/(theta_4(0,x^(15))). LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004. FORMULA G.f.: (theta_4(0, x^3)*theta_4(0, x^5))/(theta_4(0, x)*theta_4(0, x^(15))). G.f.: (E(2)*E(3)^2*E(5)^2*E(30)) / (E(1)^2*E(6)*E(10)*E(15)^2) where E(k) = prod(n>=1, 1-q^k ). - Joerg Arndt, Sep 01 2015 a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 01 2015 EXAMPLE a(5) = 14 because 10 can be written as 8+2 = 8+1+1 = 4+4+2 = 4+4+1+1 = 4+2+2+2 = 4+2+2+1+1 = 4+2+1+1+1+1 = 4+1+1+1+1+1+1 = 2+2+2+2+2 = 2+2+2+2+1+1 = 2+2+2+1+1+1+1 = 2+2+1+1+1+1+1+1 = 2+1+1+1+1+1+1+1+1 = 1+1+1+1+1+1+1+1+1+1. MAPLE series(product((1+x^k)*(1-x^(3*k))*(1-x^(5*k))*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))*(1-x^(15*k))), k=1..100), x=0, 100); MATHEMATICA nmax = 50; CoefficientList[Series[Product[(1+x^k)*(1-x^(3*k))*(1-x^(5*k))*(1+x^(15*k))/((1-x^k)*(1+x^(3*k))*(1+x^(5*k))*(1-x^(15*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 01 2015 *) PROG (PARI)  q='q+O('q^33); E(k)=eta(q^k); Vec( (E(2)*E(3)^2*E(5)^2*E(30)) / (E(1)^2*E(6)*E(10)*E(15)^2) ) \\ Joerg Arndt, Sep 01 2015 CROSSREFS Cf. A102346, A103257. Sequence in context: A277277 A241337 A103257 * A280131 A082380 A238871 Adjacent sequences:  A103256 A103257 A103258 * A103260 A103261 A103262 KEYWORD nonn AUTHOR Noureddine Chair, Feb 15 2005 EXTENSIONS Example corrected by Vaclav Kotesovec, Sep 01 2015 Maple program corrected by Vaclav Kotesovec, Sep 01 2015 STATUS approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)