A202088 Number of partitions of 5n such that cn(0,5) < cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5).

0, 0, 1, 4, 11, 25, 55, 116, 245, 505, 1026, 2030, 3936, 7450, 13837, 25210, 45206, 79831, 139136, 239471, 407582, 686346, 1144532, 1890837, 3096692, 5029412, 8104448, 12961576, 20582130, 32459992, 50859769, 79192204, 122572743

Offset: 0

Author

Max Alekseyev, Dec 11 2011

Keywords

• nonn

Comments

For a given partition, cn(i,n) means the number of its parts equal to i modulo n.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index and properties of sequences related to partitions of 5n

Crossrefs

Cf. A036888, A036893, A046776, A202087.

Programs

PARI

seq(n)={Vec(sum(k=0, n\2, x^(2*k)*(1-x^k)/prod(j=1, k, 1 - x^j + O(x*x^n))^5) + O(x*x^n), -(n+1))} \\ Andrew Howroyd, Sep 16 2019

Formula

a(n) = A036888(n) - A036893(n).

a(n) = A202087(n) - A046776(n).

G.f.: Sum_{k>=0} x^(2*k)*(1-x^k)/(Product_{j=1..k} 1 - x^j)^5. - Andrew Howroyd, Sep 16 2019

Extensions

a(0)=0 prepended by Andrew Howroyd, Sep 16 2019