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
Keywords
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
Programs
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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))
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)