A391843 a(n) = Sum_{k=0..floor(3*n/5)} binomial(k+1,3*n-5*k).

1, 0, 2, 0, 3, 1, 4, 5, 5, 15, 7, 35, 15, 70, 44, 127, 129, 221, 340, 396, 804, 781, 1742, 1716, 3550, 4005, 7009, 9390, 13835, 21421, 28033, 47107, 58993, 100283, 128136, 208982, 282569, 432197, 622575, 898064, 1357136, 1889152, 2918449, 4028036, 6204578, 8671852

Offset

0,3

Links

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

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

Formula

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

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

a(2*n) = A373961(n+1), a(2*n+1) = A373964(n+2).

Mathematica

Table[Sum[Binomial[k+1, 3*n-5*k], {k, 0, Floor[3*n/5]}], {n, 0, 46}] (* Vincenzo Librandi, Jan 19 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)/((1-x^2)^3-x^5))
(Magma) R<x>:=PowerSeriesRing(Rationals(), 55); Coefficients(R! (1-x^2) / ((1-x^2)^3 - x^5)); // Vincenzo Librandi, Jan 19 2026

Crossrefs

Cf. A390034, A392271.

Cf. A052921, A392674.

Cf. A017837, A373961, A373964.

Sequence in context: A353949 A162517 A392489 * A180876 A162170 A266770

Adjacent sequences: A391840 A391841 A391842 * A391844 A391845 A391846

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved