A390220 a(n) = Sum_{k=0..floor(n/2)} binomial(k,4*n-8*k).

1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 5, 1, 15, 1, 35, 1, 70, 2, 126, 10, 210, 46, 330, 166, 495, 496, 716, 1288, 1014, 3004, 1456, 6436, 2275, 12871, 4200, 24312, 9248, 43776, 22440, 75736, 55233, 126940, 131955, 208336, 301246, 340120, 655522, 564928, 1362935, 980629, 2718577

Offset

0,12

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)^3 / ((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(2*n) = A306752(n).

a(n) = A390221(n) - A390221(n-2).

Prog

(PARI) my(N=60, x='x+O('x^N)); Vec((1-x^2)^3/((1-x^2)^4-x^9))

Crossrefs

Cf. A390040, A390221, A390222.

Cf. A306752.

Sequence in context: A094368 A295574 A087727 * A392355 A039807 A213590

Adjacent sequences: A390217 A390218 A390219 * A390221 A390222 A390223

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 19 2026

Status

approved