A369804 Expansion of 1/(1 - x^3/(1-x)^5).

1, 0, 0, 1, 5, 15, 36, 80, 181, 431, 1060, 2617, 6401, 15521, 37513, 90741, 219918, 533619, 1295022, 3141826, 7619870, 18478155, 44810670, 108676262, 263576791, 639267800, 1550434777, 3760269946, 9119740067, 22118021213, 53642768716, 130099857234, 315531401964

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn
• easy

Comments

Number of compositions of 5*n-3 into parts 3 and 5.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,11,-5,1).

Crossrefs

Cf. A079675, A368475, A369803.

Cf. A369845, A369846, A369847, A369848.

Cf. A052920.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/(1-x^3/(1-x)^5))

PARI

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

Formula

a(n) = A052920(5*n-3) for n > 0.

a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.

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

a(n) = A369845(n) - A369845(n-1). - R. J. Mathar, Feb 14 2024