A348289 a(n) = Sum_{k=0..floor(n/8)} binomial(n-4*k,4*k).

1, 1, 1, 1, 1, 1, 1, 1, 2, 6, 16, 36, 71, 127, 211, 331, 497, 725, 1047, 1531, 2316, 3668, 6064, 10312, 17717, 30309, 51165, 84893, 138417, 222329, 353285, 558253, 881918, 1399274, 2236480, 3604588, 5853067, 9553715, 15631615, 25570103, 41734433, 67889133, 110035211, 177778263

Offset

0,9

Links

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

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

Formula

G.f.: (1-x)^3/((1-x)^4 - x^8).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-8).

Prog

(PARI) a(n) = sum(k=0, n\8, binomial(n-4*k, 4*k));
(PARI) my(N=66, x='x+O('x^N)); Vec((1-x)^3/((1-x)^4-x^8))
(Python)
from sympy import Matrix
def A348289(n):
    A = Matrix([[4, -6, 4, -1, 0, 0, 0, 1]]+[[0]*i+[1]+[0]*(7-i) for i in range(7)])
    return (A**(n-7)*Matrix([1]*8))[0] # Chai Wah Wu, Jun 15 2026

Crossrefs

Cf. A000045, A005252, A100134, A348290.

Cf. A101552.

Sequence in context: A325743 A254119 A145126 * A365733 A005676 A365735

Adjacent sequences: A348286 A348287 A348288 * A348290 A348291 A348292

Keyword

nonn,easy

Author

Seiichi Manyama, Oct 10 2021

Status

approved