A376717 Expansion of (1 - x + x^3)/((1 - x + x^3)^2 - 4*x^3).

1, 1, 1, 4, 11, 22, 42, 91, 205, 443, 936, 1999, 4316, 9300, 19949, 42785, 91917, 197548, 424331, 911218, 1957086, 4203927, 9029949, 19395031, 41657808, 89477119, 192189304, 412803240, 886657081, 1904448737, 4090567673, 8786130132, 18871714923, 40534529294

Offset: 0

Author

Seiichi Manyama, Oct 02 2024

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,2,2,0,-1).

Crossrefs

Cf. A000302, A376716, A376718.

Cf. A375278, A375279.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec((1-x+x^3)/((1-x+x^3)^2-4*x^3))

PARI

a(n) = sum(k=0, n\3, binomial(2*n-4*k+1, 2*k));

Formula

a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3) + 2*a(n-4) - a(n-6).

a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-4*k+1,2*k).