A373913 Number of compositions of 8*n into parts 7 and 8.
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
Links
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,9,-1).
Programs
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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 *) -
PARI
a(n) = sum(k=0, n\7, binomial(n+k, n-7*k));
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).