A373960 Number of compositions of 6*n-5 into parts 1 and 6.

1, 3, 12, 55, 251, 1133, 5103, 22990, 103598, 466852, 2103796, 9480387, 42721676, 192517665, 867546829, 3909446467, 17617229520, 79388930909, 357752184782, 1612146986543, 7264855441424, 32737786954481, 147527050375071, 664804576516400, 2995824317191471

Offset: 1

Author

Seiichi Manyama, Jun 23 2024

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A099242, A371125, A373302, A373958, A373959.

Cf. A005708.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+5*k, n-1-k));

Formula

a(n) = A005708(6*n-5).

a(n) = Sum_{k=0..n} binomial(n+5*k,n-1-k).

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

G.f.: x*(1-x)^4/((1-x)^6 - x).

a(n) = A373959(n) - A373959(n-1).