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

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, 40, 28, 64, 18, 52, 38, 74, 4, 16, 16, 40, 16, 48, 40, 72, 12, 48, 40, 96, 28, 88, 52, 108, 10, 40, 40, 100, 28, 96, 64, 120, 18, 72, 52, 120, 38

Offset: 0

Author

N. J. A. Sloane, Mar 01 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A001316, A071053, A134660, A134661, A134662, A255485, A247649.

Programs

Maple

r1:=proc(f) local g,n; g:=n->nops(expand(f^n) mod 2); [seq(g(n),n=0..90)]; end;
r1(1+x+x^2+x^3);

Mathematica

a[n_] := Count[(List @@ Expand[(1+x+x^3+x^4)^n]) /. x -> 1, _?OddQ]; a[0] = 1;
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Apr 04 2017 *)

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