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

0,2

Links

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

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)

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

Crossrefs

A subsequence of A001400. Cf. A274099.

Sequence in context: A202037 A322754 A224917 * A166355 A031154 A270534

Adjacent sequences: A274097 A274098 A274099 * A274101 A274102 A274103

Keyword

nonn

Author

N. J. A. Sloane, Jun 11 2016

Extensions

More terms from Colin Barker, Jun 12 2016

Status

approved