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A104274
Number of partitions of n in which odd squares occur with 2 types c,c* and with multiplicity 1. The even squares and parts that are twice the squares they occur with multiplicity 1.
2
1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 10, 10, 10, 10, 10, 10, 12, 14, 16, 18, 18, 18, 18, 18, 18, 22, 26, 28, 30, 30, 30, 30, 30, 30, 34, 38, 40, 42, 42, 42, 44, 48, 50, 54, 58, 60, 62, 62, 62, 66, 74, 78, 82, 86, 88, 90, 90, 90
OFFSET
0,2
COMMENTS
Convolution of A167700 and A167661. - Vaclav Kotesovec, Sep 19 2017
LINKS
FORMULA
G.f.: product_{k>0}((1+x^(2k-1)^2)/(1-x^(2k-1)^2)).
a(n) ~ exp(3 * 2^(-8/3) * Pi^(1/3) * ((4-sqrt(2)) * Zeta(3/2))^(2/3) * n^(1/3)) * ((4-sqrt(2)) * Zeta(3/2))^(1/3) / (2^(7/3) * sqrt(3) * Pi^(1/3) * n^(5/6)). - Vaclav Kotesovec, Sep 19 2017
EXAMPLE
E.g. a(10)=6 because we can write it as 91,91*,9*1,9*1*,82,811*.
MAPLE
series(product((1+x^((2*k-1)^2))/(1-x^(2*k-1)^2)), k=1..100), x=0, 100);
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1 + x^((2*k-1)^2)) / (1 - x^((2*k-1)^2)), {k, 1, Floor[Sqrt[nmax]/2] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 19 2017 *)
CROSSREFS
Sequence in context: A045818 A064128 A248774 * A008857 A244463 A307590
KEYWORD
easy,nonn
AUTHOR
Noureddine Chair, Feb 27 2005
STATUS
approved