A373959 Number of compositions of 6*n-4 into parts 1 and 6.

1, 4, 16, 71, 322, 1455, 6558, 29548, 133146, 599998, 2703794, 12184181, 54905857, 247423522, 1114970351, 5024416818, 22641646338, 102030577247, 459782762029, 2071929748572, 9336785189996, 42074572144477, 189601622519548, 854406199035948, 3850230516227419

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, A373960.

Cf. A005708.

Programs

PARI

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

Formula

a(n) = A005708(6*n-4).

a(n) = Sum_{k=0..n} binomial(n+1+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)^3/((1-x)^6 - x).

a(n) = A373958(n) - A373958(n-1).