A274232 Number of partitions of 2^n into at most three parts.

1, 2, 4, 10, 30, 102, 374, 1430, 5590, 22102, 87894, 350550, 1400150, 5596502, 22377814, 89494870, 357946710, 1431721302, 5726754134, 22906754390, 91626493270, 366504924502, 1466017600854, 5864066209110, 23456256447830, 93825009014102, 375300002501974

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)).

Conjectures: (Start)

a(n) = (8+3*2^(1+n)+4^n)/12 for n>0.

a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.

G.f.: (1-5*x+4*x^2+2*x^3) / ((1-x)*(1-2*x)*(1-4*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)).
b(n) = round(real((47+9*(-1)^n + 8*exp(-2/3*I*n*Pi) + 8*exp((2*I*n*Pi)/3) + 36*n+6*n^2)/72))
vector(50, n, n--; b(2^n))

Crossrefs

A subsequence of A001399. Cf. A274100, A274233.

Sequence in context: A094957 A000733 A092073 * A360322 A112846 A050397

Adjacent sequences: A274229 A274230 A274231 * A274233 A274234 A274235

Keyword

nonn

Author

Colin Barker, Jun 15 2016

Status

approved