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A373913
Number of compositions of 8*n into parts 7 and 8.
1
1, 1, 1, 1, 1, 1, 1, 2, 10, 46, 166, 496, 1288, 3004, 6437, 12888, 24464, 44728, 80428, 146320, 278104, 564929, 1225811, 2778772, 6396236, 14620646, 32760586, 71565796, 152344397, 316911454, 647536777, 1308456096, 2635130392, 5330198752, 10896635912
OFFSET
0,8
FORMULA
a(n) = A017857(8*n).
a(n) = Sum_{k=0..floor(n/7)} binomial(n+k,n-7*k).
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) + 9*a(n-7) - a(n-8).
G.f.: 1/(1 - x - x^7/(1 - x)^7).
MATHEMATICA
CoefficientList[Series[1/(1-x-x^7/(1-x)^7), {x, 0, 40}], x] (* or *) LinearRecurrence[ {8, -28, 56, -70, 56, -28, 9, -1}, {1, 1, 1, 1, 1, 1, 1, 2}, 40] (* Harvey P. Dale, Jul 29 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\7, binomial(n+k, n-7*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 22 2024
STATUS
approved