A375321 Expansion of (1 + x)^2/(1 - x^3*(1 + x)^3).

1, 2, 1, 1, 5, 10, 11, 13, 29, 57, 81, 111, 194, 352, 554, 827, 1348, 2303, 3739, 5843, 9382, 15519, 25317, 40431, 64933, 105863, 172321, 277696, 447272, 725140, 1177181, 1903186, 3072365, 4972113, 8057421, 13038606, 21075947, 34094041, 55199573, 89336141

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, A375319.

Cf. A375317,

Programs

PARI

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

PARI

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

a(n) = A375319(n) + A375319(n-1).