A373963 Number of compositions of 6*n-3 into parts 5 and 6.

0, 0, 1, 4, 10, 20, 35, 57, 94, 175, 385, 935, 2289, 5385, 12031, 25686, 53176, 108699, 223215, 465867, 991088, 2138884, 4643816, 10067197, 21695156, 46427790, 98807200, 209689343, 444983081, 946084386, 2016738335, 4308708305, 9217134511, 19720875625

Offset: 1

Author

Seiichi Manyama, Jun 24 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,7,-1).

Crossrefs

Cf. A107025, A369794, A373961, A373962, A373964.

Cf. A017837.

Programs

PARI

a(n) = sum(k=0, n\5, binomial(n+k, n-3-5*k));

Formula

a(n) = A017837(6*n-3).

a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-3-5*k).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).

G.f.: x^3*(1-x)^2/((1-x)^6 - x^5).

a(n) = A373964(n+1) - A373964(n).