A392433 a(n) = Sum_{k=0..floor(n/2)} binomial(3*k,2*n-4*k).

1, 0, 1, 3, 1, 15, 16, 37, 127, 150, 505, 1029, 1861, 5224, 9497, 21777, 50199, 98313, 232681, 490723, 1047105, 2373982, 4971986, 10993174, 24013198, 51346109, 113484808, 244619349, 531470618, 1162833495, 2510164429, 5480300644, 11910608942, 25832792982, 56331565299

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,2,6,-1,3,-3,1).

Formula

G.f.: (1 - x^2 - 3*x^3) / (1 - 2*x^2 - 6*x^3 + x^4*(1-x)^3).

a(n) = 2*a(n-2) + 6*a(n-3) - a(n-4) + 3*a(n-5) - 3*a(n-6) + a(n-7).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-x^2-3*x^3)/(1-2*x^2-6*x^3+x^4*(1-x)^3))

Crossrefs

Cf. A392431, A375307, A392432, A392434, A392435, A392436.

Sequence in context: A368493 A095922 A263632 * A284861 A284234 A365338

Adjacent sequences: A392430 A392431 A392432 * A392434 A392435 A392436

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved