A369807 Expansion of 1/(1 - x^4/(1-x)^7).

1, 0, 0, 0, 1, 7, 28, 84, 211, 476, 1029, 2276, 5384, 13594, 35371, 91667, 232681, 577710, 1413462, 3442498, 8414484, 20717963, 51346109, 127678961, 317496621, 787941379, 1950774874, 4821609252, 11910608942, 29432604429, 72787392898, 180131835001

Offset

0,6

Comments

Number of compositions of 7*n-4 into parts 4 and 7.

Links

Table of n, a(n) for n=0..31.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-34,21,-7,1).

Formula

a(n) = A369815(7*n-4) for n > 0.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 34*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.

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

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^4/(1-x)^7))
(PARI) a(n) = sum(k=0, n\4, binomial(n-1+3*k, n-4*k));

Crossrefs

Cf. A099253, A369805, A369806, A369808, A369809.

Cf. A369815.

Sequence in context: A145456 A369808 A145135 * A221141 A144900 A054469

Adjacent sequences: A369804 A369805 A369806 * A369808 A369809 A369810

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2024

Status

approved