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

%I A274232 #13 Jun 16 2016 03:14:30
%S A274232 1,2,4,10,30,102,374,1430,5590,22102,87894,350550,1400150,5596502,
%T A274232 22377814,89494870,357946710,1431721302,5726754134,22906754390,
%U A274232 91626493270,366504924502,1466017600854,5864066209110,23456256447830,93825009014102,375300002501974
%N A274232 Number of partitions of 2^n into at most three parts.
%H A274232 Colin Barker, <a href="/A274232/b274232.txt">Table of n, a(n) for n = 0..1000</a>
%F A274232 Coefficient of x^(2^n) in 1/((1-x)*(1-x^2)*(1-x^3)).
%F A274232 Conjectures: (Start)
%F A274232 a(n) = (8+3*2^(1+n)+4^n)/12 for n>0.
%F A274232 a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3) for n>3.
%F A274232 G.f.: (1-5*x+4*x^2+2*x^3) / ((1-x)*(1-2*x)*(1-4*x)).
%F A274232 (End)
%o A274232 (PARI)
%o A274232 \\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)).
%o A274232 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))
%o A274232 vector(50, n, n--; b(2^n))
%Y A274232 A subsequence of A001399. Cf. A274100, A274233.
%K A274232 nonn
%O A274232 0,2
%A A274232 _Colin Barker_, Jun 15 2016