A375319 Expansion of (1 + x)/(1 - x^3*(1 + x)^3).

1, 1, 0, 1, 4, 6, 5, 8, 21, 36, 45, 66, 128, 224, 330, 497, 851, 1452, 2287, 3556, 5826, 9693, 15624, 24807, 40126, 65737, 106584, 171112, 276160, 448980, 728201, 1174985, 1897380, 3074733, 4982688, 8055918, 13020029, 21074012, 34125561, 55210580, 89284541

Offset: 0

Author

Seiichi Manyama, Aug 12 2024

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,1,3,3,1).

Crossrefs

Cf. A115055, A375321.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec((1+x)/(1-x^3*(1+x)^3))

PARI

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

Formula

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

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