A371872 a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-2*k-1,n-3*k).

1, 1, 3, 11, 40, 147, 547, 2055, 7777, 29602, 113204, 434591, 1673821, 6464539, 25026534, 97087873, 377329971, 1468856383, 5726159811, 22351657810, 87350137071, 341726039806, 1338173763288, 5244830032639, 20573285744475, 80761011408961, 317249771957040

Offset

0,3

Links

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

Formula

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

D-finite with recurrence +n*a(n) +(-15*n+14)*a(n-1) +3*(27*n-50)*a(n-2) +2*(-93*n+259)*a(n-3) +24*(7*n-26)*a(n-4) +(-69*n+260)*a(n-5) +10*(2*n-9)*a(n-6)=0. - R. J. Mathar, Apr 22 2024

Maple

A371872 := proc(n)
    add(binomial(2*n-2*k-1, n-3*k), k=0..floor(n/3)) ;
end proc:
seq(A371872(n), n=0..60) ; # R. J. Mathar, Apr 22 2024

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*n-2*k-1, n-3*k));

Crossrefs

Cf. A360150, A371871, A371873.

Cf. A144904, A371842.

Sequence in context: A010911 A052941 A296221 * A014301 A346194 A346317

Adjacent sequences: A371869 A371870 A371871 * A371873 A371874 A371875

Keyword

nonn,changed

Author

Seiichi Manyama, Apr 10 2024

Status

approved