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A255486 Number of odd terms in expansion of (1+x+x^3+x^4)^n.

%I A255486 #15 Apr 04 2017 08:06:54
%S A255486 1,4,4,10,4,12,10,18,4,16,12,28,10,28,18,38,4,16,16,40,12,40,28,52,10,
%T A255486 40,28,64,18,52,38,74,4,16,16,40,16,48,40,72,12,48,40,96,28,88,52,108,
%U A255486 10,40,40,100,28,96,64,120,18,72,52,120,38
%N A255486 Number of odd terms in expansion of (1+x+x^3+x^4)^n.
%H A255486 Alois P. Heinz, <a href="/A255486/b255486.txt">Table of n, a(n) for n = 0..8191</a>
%p A255486 r1:=proc(f) local g,n; g:=n->nops(expand(f^n) mod 2); [seq(g(n),n=0..90)]; end;
%p A255486 r1(1+x+x^2+x^3);
%t A255486 a[n_] := Count[(List @@ Expand[(1+x+x^3+x^4)^n]) /. x -> 1, _?OddQ]; a[0] = 1;
%t A255486 Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Apr 04 2017 *)
%o A255486 (PARI) a(n) = {my(pol=(1+x+x^3+x^4)*Mod(1,2)); subst(lift(pol^n), x, 1);} \\ _Michel Marcus_, Mar 01 2015
%Y A255486 Cf. A001316, A071053, A134660, A134661, A134662, A255485, A247649.
%K A255486 nonn
%O A255486 0,2
%A A255486 _N. J. A. Sloane_, Mar 01 2015