A375316 Expansion of (1 + x)/(1 - x^2*(1 + x)^4).

1, 1, 1, 5, 11, 19, 42, 98, 205, 429, 936, 2024, 4316, 9260, 19949, 42841, 91917, 197485, 424331, 911255, 1957086, 4203998, 9029949, 19394681, 41657808, 89478064, 192189304, 412801176, 886657081, 1904452689, 4090567673, 8786123349, 18871714923, 40534539675

Offset: 0

Author

Seiichi Manyama, Aug 12 2024

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1,4,6,4,1).

Crossrefs

Cf. A093040, A375315.

Cf. A375314.

Programs

PARI

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

PARI

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

Formula

a(n) = a(n-2) + 4*a(n-3) + 6*a(n-4) + 4*a(n-5) + a(n-6).

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

a(n) = A375314(n) + A375314(n-1).