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A306752 a(n) = Sum_{k=0..n} binomial(k, 8*(n-k)). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,10
LINKS
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).
MATHEMATICA
a[n_] := Sum[Binomial[k, 8*(n-k)], {k, 0, n}]; Array[a, 38, 0] (* Amiram Eldar, Jun 21 2021 *)
PROG
(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))
CROSSREFS
Column 8 of A306680.
Cf. A017867.
Sequence in context: A140588 A137334 A209010 * A306859 A212387 A191813
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 07 2019
STATUS
approved

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)