A369803 Expansion of 1/(1 - x^2/(1-x)^5).

1, 0, 1, 5, 16, 45, 126, 361, 1046, 3032, 8771, 25348, 73252, 211724, 612009, 1769080, 5113647, 14781237, 42725841, 123501151, 356986401, 1031887518, 2982723523, 8621714049, 24921502864, 72036871920, 208226244217, 601888555723, 1739789499591, 5028950081882

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Comments

Number of compositions of 5*n-2 into parts 2 and 5.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-9,10,-5,1).

Crossrefs

Cf. A079675, A368475, A369804.

Cf. A369840, A369842, A369843, A369844.

Cf. A001687.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^5))

PARI

a(n) = sum(k=0, n\2, binomial(n-1+3*k, n-2*k));

Formula

a(n) = A001687(5*n-1) for n > 0.

a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.

a(n) = Sum_{k=0..floor(n/2)} binomial(n-1+3*k,n-2*k).

a(n) = A369840(n)-A369840(n-1). - R. J. Mathar, Feb 14 2024