A369813 Expansion of 1/(1 - x^2 - x^7).

1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 2, 5, 4, 6, 7, 7, 11, 9, 16, 13, 22, 20, 29, 31, 38, 47, 51, 69, 71, 98, 102, 136, 149, 187, 218, 258, 316, 360, 452, 509, 639, 727, 897, 1043, 1257, 1495, 1766, 2134, 2493, 3031, 3536, 4288, 5031, 6054, 7165, 8547, 10196, 12083, 14484, 17114, 20538, 24279, 29085, 34475

Offset: 0

Author

Seiichi Manyama, Feb 02 2024

Keywords

• nonn
• easy

Comments

Number of compositions of n into parts 2 and 7.

Links

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

Crossrefs

Cf. A005709, A017847, A369814, A369815, A369816.

Cf. A007380.

Programs

Mathematica

CoefficientList[Series[1/(1-x^2-x^7),{x,0,80}],x] (* or *) LinearRecurrence[{0,1,0,0,0,0,1},{1,0,1,0,1,0,1},80] (* Harvey P. Dale, Dec 04 2024 *)

PARI

my(N=70, x='x+O('x^N)); Vec(1/(1-x^2-x^7))

PARI

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

Formula

a(n) = a(n-2) + a(n-7).

a(n) = A007380(n-7) for n >= 8.