A306860 a(n) = Sum_{k=0..floor(n/9)} binomial(n,9*k).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 56, 221, 716, 2003, 5006, 11441, 24311, 48622, 92398, 168151, 295261, 504736, 850840, 1442101, 2523676, 4686826, 9373652, 20030039, 44612702, 100804436, 226444616, 499685777, 1076832989, 2261792303, 4631710931, 9263421862

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 (9,-36,84,-126,126,-84,36,-9,2).

Crossrefs

Column 9 of A306846.

Programs

Mathematica

a[n_] := Sum[Binomial[n, 9*k], {k, 0, Floor[n/9]}]; Array[a, 40, 0] (* Amiram Eldar, Jun 13 2021 *)

PARI

{a(n) = sum(k=0, n\9, binomial(n, 9*k))}

PARI

N=66; x='x+O('x^N); Vec((1-x)^8/((1-x)^9-x^9))

Formula

G.f.: (1 - x)^8/((1 - x)^9 - x^9).

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + 2*a(n-9) for n > 8.