A371871 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k-2,n-3*k).

1, 0, 1, 5, 18, 66, 246, 924, 3493, 13277, 50697, 194327, 747319, 2882061, 11142027, 43167573, 167561586, 651513594, 2537041938, 9892847952, 38623197264, 150959213886, 590626854072, 2312979822738, 9065733950526, 35561306875380, 139595183125750

Offset

0,4

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = [x^n] 1/((1-x^3) * (1-x)^(n-1)).

D-finite with recurrence 9*n*a(n) +3*(-17*n+16)*a(n-1) +3*(21*n-50)*a(n-2) +(-17*n+16)*a(n-3) +10*(2*n-5)*a(n-4)=0. - R. J. Mathar, Apr 22 2024

Maple

A371871 := proc(n)
    1/(1-x^3)/(1-x)^(n-1) ;
    coeftayl(%, x=0, n) ;
end proc:
seq(A371871(n), n=0..60) ; # R. J. Mathar, Apr 22 2024

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k-2, n-3*k));

Crossrefs

Cf. A360150, A371872, A371873.

Cf. A105872, A371758.

Sequence in context: A051944 A153373 A225015 * A166677 A318062 A158879

Adjacent sequences: A371868 A371869 A371870 * A371872 A371873 A371874

Keyword

nonn

Author

Seiichi Manyama, Apr 10 2024

Status

approved