A373907 Number of compositions of 7*n into parts 1 and 7.

1, 2, 10, 53, 264, 1294, 6349, 31200, 153366, 753836, 3705166, 18211117, 89508951, 439943336, 2162355196, 10628140702, 52238121106, 256754344524, 1261967164192, 6202664757387, 30486569842400, 149843813435961, 736493759087077, 3619922936674360

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (8,-21,35,-35,21,-7,1).

Formula

a(n) = A005709(7*n).

a(n) = Sum_{k=0..n} binomial(n+6*k,n-k).

a(n) = 8*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: 1/(1 - x - x/(1 - x)^6).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+6*k, n-k));

Crossrefs

Cf. A373908, A373909, A373910, A373911, A373912.

Cf. A005709, A369836.

Sequence in context: A080118 A086546 A057415 * A037724 A037619 A221610

Adjacent sequences: A373904 A373905 A373906 * A373908 A373909 A373910

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 22 2024

Status

approved