A306852 a(n) = Sum_{k=0..floor(n/7)} binomial(n,7*k).

1, 1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1717, 3434, 6451, 11561, 20129, 34885, 62017, 116281, 232562, 490337, 1062601, 2309385, 4950751, 10381281, 21242341, 42484682, 83411715, 161766061, 312168761, 603861897, 1178135905, 2326683921, 4653367842

Offset: 0

Author

Seiichi Manyama, Mar 14 2019

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,2).

Crossrefs

Column 7 of A306846.

Programs

Mathematica

a[n_] := Sum[Binomial[n,7*k], {k,0,Floor[n/7]}]; Array[a, 36, 0] (* Amiram Eldar, May 25 2021 *)

PARI

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

PARI

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

Formula

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

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) + 2*a(n-7) for n > 6.