A202087 Number of partitions of 5n such that cn(0,5) <= cn(1,5) = cn(4,5) = cn(2,5) = cn(3,5).

1, 0, 1, 5, 16, 40, 91, 191, 391, 776, 1521, 2921, 5537, 10301, 18888, 34061, 60568, 106162, 183778, 314258, 531573, 889779, 1475249, 2423709, 3948471, 6380559, 10232772, 16291635, 25759898, 40462162, 63156523, 97984149, 151139494

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..999
• Index and properties of sequences related to partitions of 5n

Crossrefs

Cf. A036880, A036883, A046776, A202088.

Programs

PARI

seq(n)={Vec(sum(k=0, n\2, x^(2*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) = A036880(n) - A036883(n).

a(n) = A046776(n) + A202088(n).

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

Extensions

a(0)=1 prepended by Andrew Howroyd, Sep 16 2019