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.

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

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

Cf. A080054, A292563.

Sequence in context: A045818 A064128 A248774 * A008857 A244463 A307590

Adjacent sequences: A104271 A104272 A104273 * A104275 A104276 A104277

Keyword

easy,nonn

Author

Noureddine Chair, Feb 27 2005

Status

approved