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

1,4

Links

Table of n, a(n) for n=1..34.

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

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).

Prog

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

Crossrefs

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

Cf. A017837.

Sequence in context: A266353 A390044 A139748 * A392553 A137359 A134987

Adjacent sequences: A373960 A373961 A373962 * A373964 A373965 A373966

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 24 2024

Status

approved