A375364 Expansion of 1/( (1 + x) * (1 - x^2*(1 + x)^3) ).

1, -1, 2, 1, 3, 4, 12, 17, 35, 67, 127, 234, 451, 850, 1602, 3031, 5740, 10837, 20490, 38751, 73253, 138471, 261814, 494972, 935738, 1769079, 3344568, 6323022, 11953992, 22599700, 42725842, 80775309, 152709941, 288705926, 545813095, 1031887517, 1950836006

Offset: 0

Author

Seiichi Manyama, Aug 13 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A375315, A375317, A375365.

Programs

PARI

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

PARI

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

Formula

a(n) = -a(n-1) + 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(3*k-1,n-2*k).

a(n) = A375365(n) + A375365(n-1).