A369806 Expansion of 1/(1 - x^3/(1-x)^7).

1, 0, 0, 1, 7, 28, 85, 224, 567, 1485, 4117, 11802, 33909, 96182, 269402, 750275, 2090728, 5845015, 16384908, 45973701, 128944042, 361364501, 1012168575, 2834690172, 7939970075, 22244001961, 62323608147, 174620915138, 489240430938, 1370662332271, 3839992876850

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Comments

Number of compositions of 7*n-3 into parts 3 and 7.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,36,-35,21,-7,1).

Crossrefs

Cf. A099253, A369805, A369807, A369808, A369809.

Cf. A369814.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/(1-x^3/(1-x)^7))

PARI

a(n) = sum(k=0, n\3, binomial(n-1+4*k, n-3*k));

Formula

a(n) = A369814(7*n-3) for n > 0.

a(n) = 7*a(n-1) - 21*a(n-2) + 36*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.

a(n) = Sum_{k=0..floor(n/3)} binomial(n-1+4*k,n-3*k).