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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
OFFSET
0,2
COMMENTS
Convolution of A261796 and A261797. - Vaclav Kotesovec, Sep 01 2015
LINKS
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) = Product_{n>=1} 1-q^(k*n). - 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
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