A369814 Expansion of 1/(1 - x^3 - x^7).

1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 0, 1, 3, 1, 1, 4, 3, 1, 5, 6, 2, 6, 10, 5, 7, 15, 11, 9, 21, 21, 14, 28, 36, 25, 37, 57, 46, 51, 85, 82, 76, 122, 139, 122, 173, 224, 204, 249, 346, 343, 371, 519, 567, 575, 768, 913, 918, 1139, 1432, 1485, 1714, 2200, 2398, 2632, 3339, 3830, 4117, 5053, 6030, 6515, 7685

Offset: 0

Author

Seiichi Manyama, Feb 02 2024

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 3 and 7.

Links

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

Crossrefs

Cf. A005709, A017847, A369813, A369815, A369816.

Programs

PARI

my(N=80, x='x+O('x^N)); Vec(1/(1-x^3-x^7))

PARI

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

Formula

a(n) = a(n-3) + a(n-7).