A392402 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k,3*k).

1, 1, 1, 2, 11, 36, 86, 194, 497, 1381, 3739, 9693, 24901, 64933, 171112, 450017, 1177181, 3074733, 8044478, 21075947, 55210580, 144535714, 378292930, 990284337, 2592800365, 6788565211, 17772694549, 46527959417, 121809999497, 318905310816, 834913179137

Offset

0,4

Links

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

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

Formula

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

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

Prog

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

Crossrefs

Cf. A387843, A392400, A392401, A392403, A392404, A392405.

Sequence in context: A184538 A392404 A316322 * A238706 A071244 A005583

Adjacent sequences: A392399 A392400 A392401 * A392403 A392404 A392405

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 10 2026

Status

approved