A371458 Expansion of 1/(1 - x/(1 - 9*x^3)^(1/3)).

1, 1, 1, 1, 4, 7, 10, 31, 61, 100, 274, 565, 1000, 2551, 5380, 10000, 24376, 52018, 100000, 236389, 507706, 1000000, 2313346, 4986178, 10000000, 22773334, 49180165, 100000000, 225092416, 486575935, 1000000000, 2231117230, 4824998773, 10000000000

Offset: 0

Author

Seiichi Manyama, Jun 07 2024

Keywords

• nonn

Crossrefs

Cf. A362206, A371456.

Cf. A066872, A098615, A373510, A373511.

Programs

Maple

A371458 := proc(n)
    add(9^k*binomial(n/3-1,k),k=0..floor(n/3)) ;
end proc:
seq(A371458(n),n=0..70) ; # R. J. Mathar, Jun 07 2024

PARI

a(n) = sum(k=0, n\3, 9^k*binomial(n/3-1, k));

Formula

a(3*n) = 10^(n-1) for n > 0.

a(n) = Sum_{k=0..floor(n/3)} 9^k * binomial(n/3-1,k).

D-finite with recurrence (n-1)*(n-2)*a(n) +4*(-7*n^2+48*n-86)*a(n-3) +9*(29*n-141)*(n-6)*a(n-6) -810*(n-6)*(n-9)*a(n-9)=0. - R. J. Mathar, Jun 07 2024

a(n) == 1 (mod 3). - Seiichi Manyama, Jun 11 2024