A306721 a(n) = Sum_{k=0..n} binomial(k, 7*(n-k)).

1, 1, 1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1717, 3433, 6437, 11456, 19569, 32505, 53449, 89149, 155041, 286825, 564929, 1163317, 2442210, 5117225, 10558381, 21308121, 41973391, 80778601, 152344397, 282855561, 520060249, 953217792, 1753553441, 3256528177, 6127896977, 11694334137

Offset: 0

Author

Seiichi Manyama, Mar 06 2019

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3556
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1,1).

Crossrefs

Column 7 of A306680.

Cf. A017857.

Programs

Mathematica

a[n_] := Sum[Binomial[k, 7*(n-k)], {k, 0, n}]; Array[a, 40, 0] (* Amiram Eldar, Jun 21 2021 *)

PARI

{a(n) = sum(k=0, n, binomial(k, 7*(n-k)))}

PARI

N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7-x^8))

Formula

G.f.: (1-x)^6/((1-x)^7-x^8).

a(n) = 7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+21*a(n-5)-7*a(n-6)+a(n-7)+a(n-8) for n > 7.

a(n) = A017857(7*n).