A392432 a(n) = Sum_{k=0..floor(2*n/3)} binomial(3*k,2*n-3*k).

1, 0, 3, 2, 15, 24, 86, 192, 546, 1381, 3651, 9582, 24901, 65748, 170796, 450017, 1172412, 3080367, 8044478, 21096027, 55169988, 144535714, 378243264, 990489234, 2592800365, 6788471991, 17771977254, 46527959417, 121812102840, 318906184152, 834913179137

Offset

0,3

Links

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

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

Formula

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

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

Prog

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

Crossrefs

Cf. A392431, A375307, A392433, A392434, A392435, A392436.

Sequence in context: A133932 A111999 A286947 * A334559 A190961 A346059

Adjacent sequences: A392429 A392430 A392431 * A392433 A392434 A392435

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved