A390219 a(n) = Sum_{k=0..floor(4*n/7)} binomial(k+2,4*n-7*k).

1, 0, 3, 0, 6, 0, 10, 1, 15, 7, 21, 28, 28, 84, 37, 210, 56, 462, 121, 924, 352, 1717, 1079, 3018, 3094, 5125, 8113, 8688, 19569, 15436, 43913, 30192, 92721, 65892, 186257, 155041, 360221, 374057, 680505, 892079, 1278893, 2064503, 2442210, 4606946, 4831338, 9915530, 9999238

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,1,-1).

Formula

G.f.: (1-x^2) / ((1-x^2)^4 - x^7).

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

a(n) = A390039(n) - A390039(n-2).

Mathematica

CoefficientList[Series[(1-x^2)/((1-x^2)^4-x^7), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 20 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)/((1-x^2)^4-x^7))
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x^2) / ((1-x^2)^4 - x^7)); // Vincenzo Librandi, Jan 20 2026

Crossrefs

Cf. A390039, A390218, A392355.

Sequence in context: A390222 A007385 A390035 * A392255 A352610 A307644

Adjacent sequences: A390216 A390217 A390218 * A390220 A390221 A390222

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved