A392434 a(n) = Sum_{k=0..floor(2*n/5)} binomial(3*k,2*n-5*k).

1, 0, 0, 3, 1, 1, 15, 15, 10, 84, 127, 102, 496, 939, 950, 3070, 6589, 8065, 19950, 45193, 64109, 135120, 307616, 487492, 941887, 2096251, 3598606, 6675696, 14367175, 26051277, 47676838, 99202464, 186268756, 341203236, 689946694, 1321966300, 2439715534

Offset

0,4

Links

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

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

Formula

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

a(n) = 6*a(n-3) + 2*a(n-4) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8).

Mathematica

LinearRecurrence[{0, 0, 6, 2, 1, -3, 3, -1}, {1, 0, 0, 3, 1, 1, 15, 15}, 50] (* Vincenzo Librandi, Jan 13 2026 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec((1-3*x^3-x^4)/(1-6*x^3-2*x^4-x^5*(1-x)^3))
(Magma) I:=[1, 0, 0, 3, 1, 1, 15, 15]; [n le 8 select I[n] else 6*Self(n-3) + 2*Self(n-4) + Self(n-5) - 3*Self(n-6) + 3*Self(n-7) - Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 13 2026

Crossrefs

Cf. A392431, A375307, A392432, A392433, A392435, A392436.

Sequence in context: A174410 A156690 A228900 * A060325 A087987 A383613

Adjacent sequences: A392431 A392432 A392433 * A392435 A392436 A392437

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 11 2026

Status

approved