A373934 Number of compositions of 7*n-2 into parts 6 and 7.
0, 1, 3, 6, 10, 15, 21, 29, 46, 100, 275, 781, 2080, 5097, 11562, 24583, 49725, 97376, 188480, 368734, 742811, 1553192, 3353332, 7372536, 16261025, 35583926, 76806997, 163327279, 342902007, 713848316, 1481274767, 3078928619, 6433465844, 13534471164
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-6,1).
Programs
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PARI
a(n) = sum(k=0, n\6, binomial(n+k, n-2-6*k));
Formula
a(n) = A017847(7*n-2).
a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-2-6*k).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 6*a(n-6) + a(n-7).
G.f.: x^2*(1-x)^4/((1-x)^7 - x^6).