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 A103257 Number of partitions of 2n free of multiples of 5. All odd parts occur with multiplicity 2 or 4. the even parts occur at most twice. 4
 1, 2, 4, 6, 10, 14, 20, 28, 40, 54, 72, 96, 126, 164, 212, 272, 346, 436, 548, 684, 850, 1052, 1296, 1588, 1940, 2362, 2864, 3462, 4172, 5012, 6004, 7172, 8548, 10160, 12048, 14256, 16830, 19828, 23312, 27356, 32040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Convolution of A261796 and A261797. - Vaclav Kotesovec, Sep 01 2015 LINKS Robert Israel, 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). G.f.: E(2)*E(3)^2*E(5)^2) / (E(1)^2*E(6)*E(10)) where E(k) = prod(n>=1, 1-q^k ). - Joerg Arndt, Sep 01 2015 a(n) ~ exp(Pi*sqrt(7*n/15)) / sqrt(15*n). - Vaclav Kotesovec, Sep 01 2015 EXAMPLE E.g. a(5) = 14 because 10 can be written as 8+2 = 8+1+1 = 6+4 = 6+2+2 = 6+2+1+1 = 6+1+1+1+1 = 4+4+2 = 4+4+1+1 = 4+3+3 = 4+2+2+1+1 = 4+2+1+1+1+1 = 3+3+2+2 = 3+3+2+1+1 = 3+3+1+1+1+1. MAPLE series(product(((1+x^k)*(1-x^(3*k))*(1-x^(5*k)))/((1-x^k)*(1+x^(3*k))*(1+x^(5*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^k)*(1+x^(3*k))*(1+x^(5*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(1)^2*E(6)*E(10)) ) \\ Joerg Arndt, Sep 01 2015 CROSSREFS Cf. A098151, A261796, A261797. Sequence in context: A268752 A277277 A241337 * A103259 A280131 A082380 Adjacent sequences:  A103254 A103255 A103256 * A103258 A103259 A103260 KEYWORD nonn AUTHOR Noureddine Chair, Jan 27 2005 EXTENSIONS Example corrected by Vaclav Kotesovec, Sep 01 2015 Maple program fixed by Vaclav Kotesovec, Sep 01 2015 STATUS approved

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)