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A373890
Number of compositions of 8*n into parts 1 and 8.
1
1, 2, 11, 64, 345, 1824, 9661, 51284, 272333, 1445995, 7677250, 40760798, 216412235, 1149004281, 6100444144, 32389272248, 171965334801, 913020717480, 4847528344990, 25737127996244, 136646907481155, 725503534206186, 3851937726561990, 20451208781128462
OFFSET
0,2
FORMULA
a(n) = A005710(8*n).
a(n) = Sum_{k=0..n} binomial(n+7*k,n-k).
a(n) = 9*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).
G.f.: 1/(1 - x - x/(1 - x)^7).
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+7*k, n-k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 22 2024
STATUS
approved