A306752 a(n) = Sum_{k=0..n} binomial(k, 8*(n-k)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 10, 46, 166, 496, 1288, 3004, 6436, 12871, 24312, 43776, 75736, 126940, 208336, 340120, 564928, 980629, 1817047, 3605252, 7531836, 16146326, 34716826, 73737316, 153430156, 311652271, 617594122, 1195477615, 2266064352, 4221317464

Offset: 0

Author

Seiichi Manyama, Mar 07 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3528
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1,1).

Crossrefs

Column 8 of A306680.

Cf. A017867.

Programs

Mathematica

a[n_] := Sum[Binomial[k, 8*(n-k)], {k, 0, n}]; Array[a, 38, 0] (* Amiram Eldar, Jun 21 2021 *)

PARI

{a(n) = sum(k=0, n, binomial(k, 8*(n-k)))}

PARI

N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8-x^9))

Formula

G.f.: (1-x)^7/((1-x)^8 - x^9).

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) + a(n-9) for n > 8.

a(n) = A017867(8*n).