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

1,2

Links

Table of n, a(n) for n=1..25.

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

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).

Prog

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

Crossrefs

Cf. A099242, A371125, A373302, A373958, A373960.

Cf. A005708.

Sequence in context: A091354 A326654 A246014 * A231373 A161797 A124533

Adjacent sequences: A373956 A373957 A373958 * A373960 A373961 A373962

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 23 2024

Status

approved