A373302 Number of compositions of 6*n-2 into parts 1 and 6.

1, 6, 27, 119, 533, 2402, 10829, 48804, 219925, 991044, 4465957, 20125051, 90690002, 408678475, 1841637299, 8299012941, 37398034921, 168527634148, 759439995404, 3422282105232, 15421909405056, 69496108849357, 313171930813206, 1411253951813003, 6359566489040219

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, A373958, A373959, A373960.

Cf. A005708, A373928.

Programs

PARI

a(n) = sum(k=0, n, binomial(n+3+5*k, n-1-k));

Formula

a(n) = A005708(6*n-2).

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

a(n) = A099242(n-1) - A099242(n-2).