A390221 a(n) = Sum_{k=0..floor(n/2)} binomial(k+1,4*n-8*k+1).

1, 0, 2, 0, 3, 0, 4, 0, 5, 1, 6, 6, 7, 21, 8, 56, 9, 126, 11, 252, 21, 462, 67, 792, 233, 1287, 729, 2003, 2017, 3017, 5021, 4473, 11457, 6748, 24328, 10948, 48640, 20196, 92416, 42636, 168152, 97869, 295092, 229824, 503428, 531070, 843548, 1186592, 1408476

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,-6,0,4,0,-1,1).

Formula

G.f.: (1-x^2)^2 / ((1-x^2)^4 - x^9).

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) - a(n-8) + a(n-9).

a(n) = A390222(n) - A390222(n-2).

Mathematica

CoefficientList[Series[(1-x^2)^2/((1-x^2)^4-x^9), {x, 0, 50}], x] (* Vincenzo Librandi, Jan 20 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)^2/((1-x^2)^4-x^9))
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x^2)^2 / ((1-x^2)^4 - x^9)); // Vincenzo Librandi, Jan 20 2026

Crossrefs

Cf. A390040, A390220, A390222.

Sequence in context: A008722 A008736 A263396 * A029180 A008802 A008809

Adjacent sequences: A390218 A390219 A390220 * A390222 A390223 A390224

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved