A274272 Number of partitions of 5^n into at most four parts.

1, 6, 185, 15246, 1736385, 212946246, 26516391385, 3312004971246, 413937039016385, 51740540399346246, 6467527813385891385, 808439983261977471246, 101054973072475964016385, 12631871013177766274346246, 1578983861125177809948391385

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..450

Formula

Coefficient of x^(5^n) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Conjectures (Start)

a(n) = (57+8*(-1)^n+63*5^n+3*5^(1+2*n)+125^n)/144.

a(n) = 155*a(n-1)-3874*a(n-2)+15470*a(n-3)+3875*a(n-4)-15625*a(n-5) for n>4.

G.f.: (1-149*x+3129*x^2-5655*x^3-6750*x^4) / ((1-x)*(1+x)*(1-5*x)*(1-25*x)*(1-125*x)).

(End)

Prog

(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
b(n) = round(real(68+36*(-1)^n+18*((-I)^n+I^n)+(16*exp(-2/3*I*n*Pi)*(1+I*sqrt(3)+2*exp((4*I*n*Pi)/3)))/(1+(-1)^(1/3))+59*(1+n)+9*(-1)^n*(1+n)+18*(1+n)*(2+n)+2*(1+n)*(2+n)*(3+n))/288)
vector(20, n, n--; b(5^n))

Crossrefs

A subsequence of A001400.

Cf. A274100 (2^n), A274271 (3^n).

Sequence in context: A012208 A012181 A012224 * A175237 A222335 A037298

Adjacent sequences: A274269 A274270 A274271 * A274273 A274274 A274275

Keyword

nonn

Author

Colin Barker, Jun 17 2016

Status

approved