A369805 Expansion of 1/(1 - x^2/(1-x)^7).

1, 0, 1, 7, 29, 98, 316, 1043, 3536, 12083, 41168, 139750, 473824, 1607014, 5453022, 18506947, 62808496, 213144034, 723295969, 2454483506, 8329290739, 28265565587, 95919580313, 325504019213, 1104600373788, 3748469764612, 12720462563684, 43166996581876

Offset

0,4

Comments

Number of compositions of 7*n-2 into parts 2 and 7 for n > 0. - Seiichi Manyama, Jul 07 2026

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-20,35,-35,21,-7,1).

Formula

a(n) = A369813(7*n-2) for n > 0.

a(n) = 7*a(n-1) - 20*a(n-2) + 35*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/2)} binomial(n-1+5*k,n-2*k).

Mathematica

CoefficientList[Series[1/(1-x^2/(1-x)^7), {x, 0, 30}], x] (* Harvey P. Dale, Jul 05 2026 *)
(* Alternative: *)
LinearRecurrence[{7, -20, 35, -35, 21, -7, 1}, {1, 0, 1, 7, 29, 98, 316, 1043}, 30] (* Harvey P. Dale, Jul 05 2026 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^7))
(PARI) a(n) = sum(k=0, n\2, binomial(n-1+5*k, n-2*k));

Crossrefs

Cf. A099253, A369806, A369807, A369808, A369809.

Cf. A369813.

Sequence in context: A042609 A002941 A193655 * A227086 A102485 A246038

Adjacent sequences: A369802 A369803 A369804 * A369806 A369807 A369808

Keyword

nonn

Author

Seiichi Manyama, Feb 01 2024

Status

approved