A373958 Number of compositions of 6*n-3 into parts 1 and 6.

1, 5, 21, 92, 414, 1869, 8427, 37975, 171121, 771119, 3474913, 15659094, 70564951, 317988473, 1432958824, 6457375642, 29099021980, 131129599227, 590912361256, 2662842109828, 11999627299824, 54074199444301, 243675821963849, 1098082020999797, 4948312537227216

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, A373959, A373960.

Cf. A005708.

Programs

Mathematica

LinearRecurrence[{7,-15,20,-15,6,-1},{1,5,21,92,414,1869},30] (* Harvey P. Dale, Nov 04 2024 *)

PARI

a(n) = sum(k=0, n, binomial(n+2+5*k, n-1-k));

Formula

a(n) = A005708(6*n-3).

a(n) = Sum_{k=0..n} binomial(n+2+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)^2/((1-x)^6 - x).

a(n) = A373302(n) - A373302(n-1).