A369816 Expansion of 1/(1 - x^5 - x^7).

1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 1, 0, 3, 0, 3, 1, 1, 4, 0, 6, 1, 4, 5, 1, 10, 1, 10, 6, 5, 15, 2, 20, 7, 15, 21, 7, 35, 9, 35, 28, 22, 56, 16, 70, 37, 57, 84, 38, 126, 53, 127, 121, 95, 210, 91, 253, 174, 222, 331, 186, 463, 265, 475, 505, 408, 794, 451, 938, 770, 883, 1299, 859, 1732, 1221

Offset: 0

Author

Seiichi Manyama, Feb 02 2024

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 5 and 7.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1,0,1).

Crossrefs

Cf. A005709, A017847, A369813, A369814, A369815.

Programs

PARI

my(N=80, x='x+O('x^N)); Vec(1/(1-x^5-x^7))

PARI

a(n) = sum(k=0, n\7, ((n-2*k)%5==0)*binomial((n-2*k)/5, k));

Formula

a(n) = a(n-5) + a(n-7).

G.f.: 1/((1-x+x^2)*(1+x-x^3-x^4-x^5)). - R. J. Mathar, Jul 03 2024