A373935 Number of compositions of 7*n-3 into parts 6 and 7.
0, 0, 1, 4, 10, 20, 35, 56, 85, 131, 231, 506, 1287, 3367, 8464, 20026, 44609, 94334, 191710, 380190, 748924, 1491735, 3044927, 6398259, 13770795, 30031820, 65615746, 142422743, 305750022, 648652029, 1362500345, 2843775112, 5922703731, 12356169575
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-3-6*k));
Formula
a(n) = A017847(7*n-3).
a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-3-6*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^3*(1-x)^3/((1-x)^7 - x^6).