A392403 a(n) = Sum_{k=0..floor(2*n/7)} binomial(2*n-4*k,3*k).

1, 1, 1, 1, 5, 21, 57, 122, 249, 575, 1485, 3830, 9369, 22107, 52226, 125925, 307653, 750275, 1815191, 4371772, 10539893, 25488736, 61735922, 149450118, 361364501, 873306464, 2111040783, 5105279903, 12348599802, 29865304188, 72217700805, 174620915138

Offset

0,5

Links

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

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

Formula

G.f.: ((1-x)^2 - 2*x^4) / ((1-x)^3 - 6*x^4 - 2*x^5 - x^7).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + 6*a(n-4) + 2*a(n-5) + a(n-7).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(((1-x)^2-2*x^4)/((1-x)^3-6*x^4-2*x^5-x^7))

Crossrefs

Cf. A387843, A392400, A392401, A392402, A392404, A392405.

Sequence in context: A033275 A166464 A392405 * A059859 A146617 A392401

Adjacent sequences: A392400 A392401 A392402 * A392404 A392405 A392406

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 10 2026

Status

approved