A369815 Expansion of 1/(1 - x^4 - x^7).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 3, 1, 0, 3, 4, 1, 1, 6, 5, 1, 4, 10, 6, 2, 10, 15, 7, 6, 20, 21, 9, 16, 35, 28, 15, 36, 56, 37, 31, 71, 84, 52, 67, 127, 121, 83, 138, 211, 173, 150, 265, 332, 256, 288, 476, 505, 406, 553, 808, 761, 694, 1029, 1313, 1167, 1247, 1837, 2074, 1861, 2276, 3150, 3241

Offset: 0

Author

Seiichi Manyama, Feb 02 2024

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 4 and 7.

Links

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

Crossrefs

Cf. A005709, A017847, A369813, A369814, A369816.

Programs

PARI

my(N=80, x='x+O('x^N)); Vec(1/(1-x^4-x^7))

PARI

a(n) = sum(k=0, n\7, ((n-3*k)%4==0)*binomial((n-3*k)/4, k));

Formula

a(n) = a(n-4) + a(n-7).