A390039 a(n) = Sum_{k=0..floor(4*n/7)} binomial(k+3,4*n-7*k).

1, 0, 4, 0, 10, 0, 20, 1, 35, 8, 56, 36, 84, 120, 121, 330, 177, 792, 298, 1716, 650, 3433, 1729, 6451, 4823, 11576, 12936, 20264, 32505, 35700, 76418, 65892, 169139, 131784, 355396, 286825, 715617, 660882, 1396122, 1552961, 2675015, 3617464, 5117225, 8224410

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 / ((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).

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(1/((1-x^2)^4-x^7))

Crossrefs

Cf. A390041.

Sequence in context: A390323 A390040 A164735 * A382522 A293933 A345057

Adjacent sequences: A390036 A390037 A390038 * A390040 A390041 A390042

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2026

Status

approved