%I
%S 1,0,0,0,0,1,0,1,2,1,3,5,4,9,13,14,26,36,45,75,103,
%T 139,217,300,420,631,881,1254,1843,2596,3720,5401,7658,
%U 10998,15864,22594,32459,46664,66649,95718,137383,196557,282155
%N a(n+1) = a(n1) + 2 a(n2)  a(n4) ; a(0)=1, a(n)=0 for 0 < n < 5;
%C a(n) is the constant term of the canonical representative (polynomial of degree < 5) of x^n (mod x^5x^32*x^2+1), see example.
%F G.f.: sum( a(k) x^k, k=0...oo ) = (1  x^2  2*x^3)/(1  x^2  2*x^3 + x^5)
%e x^6 = x^4 + 2*x^3  x (mod x^5  x^3  2*x^2 + 1), and the l.h.s. has no constant term, so a(6) = 0.
%e x^14 = 14*x^4 + 26*x^3 + 22*x^2  9*x  13 (mod x^5  x^3  2*x^2 + 1), and the constant term on the r.h.s. is a(14) = 13.
%o (PARI) a(n) = polcoeff( lift( Mod( x, x^5x^32*x^2+1)^n),0)
%K easy,sign
%O 0,9
%A _M. F. Hasler_, Nov 04 2010
