A392431 a(n) = Sum_{k=0..2*n} binomial(3*k,2*n-k).

1, 4, 26, 181, 1252, 8657, 59864, 413966, 2862617, 19795288, 136886433, 946583628, 6545722210, 45264335853, 313007493212, 2164478699633, 14967590689568, 103502414271126, 715729737814001, 4949344043795952, 34225218220881473, 236670870301545236, 1636603176283509034

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (7,-1,3,-1).

Formula

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

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

a(n) = A003269(6*n+1).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1-3*x-x^2)/(1-6*x-2*x^2-x*(1-x)^3))

Crossrefs

Cf. A375307, A392432, A392433, A392434, A392435, A392436.

Cf. A003269.

Sequence in context: A390424 A199490 A116429 * A084134 A098443 A264226

Adjacent sequences: A392428 A392429 A392430 * A392432 A392433 A392434

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved