A274100 Number of partitions of 2^n into at most four parts.

1, 2, 5, 15, 64, 351, 2280, 16335, 123464, 959631, 7566280, 60090255, 478968264, 3824743311, 30569959880, 244447781775, 1955134763464, 15639288341391, 125107148059080, 1000828550570895, 8006513870533064, 64051652831273871, 512411390124519880

Offset: 0

Author

N. J. A. Sloane, Jun 11 2016

Keywords

• nonn

Links

• Colin Barker, Table of n, a(n) for n = 0..1000

Crossrefs

A subsequence of A001400. Cf. A274099.

Programs

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(50, n, n--; b(2^n)) \\ Colin Barker, Jun 12 2016

Formula

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

Conjectures from Colin Barker, Jun 12 2016: (Start)

a(n) = 14*a(n-1)-55*a(n-2)+50*a(n-3)+56*a(n-4)-64*a(n-5) for n>6.

G.f.: (1-12*x+32*x^2+5*x^3-27*x^4-18*x^5-16*x^6) / ((1-x)*(1+x)*(1-2*x)*(1-4*x)*(1-8*x)).

(End)

Extensions

More terms from Colin Barker, Jun 12 2016