cp's OEIS Frontend

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

%I A274100 #21 Jun 15 2016 11:59:33
%S A274100 1,2,5,15,64,351,2280,16335,123464,959631,7566280,60090255,478968264,
%T A274100 3824743311,30569959880,244447781775,1955134763464,15639288341391,
%U A274100 125107148059080,1000828550570895,8006513870533064,64051652831273871,512411390124519880
%N A274100 Number of partitions of 2^n into at most four parts.
%H A274100 Colin Barker, <a href="/A274100/b274100.txt">Table of n, a(n) for n = 0..1000</a>
%F A274100 Coefficient of x^(2^n) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
%F A274100 Conjectures from _Colin Barker_, Jun 12 2016: (Start)
%F A274100 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.
%F A274100 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)).
%F A274100 (End)
%o A274100 (PARI)
%o A274100 \\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
%o A274100 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))
%o A274100 vector(50, n, n--; b(2^n)) \\ _Colin Barker_, Jun 12 2016
%Y A274100 A subsequence of A001400. Cf. A274099.
%K A274100 nonn
%O A274100 0,2
%A A274100 _N. J. A. Sloane_, Jun 11 2016
%E A274100 More terms from _Colin Barker_, Jun 12 2016