A373937 Number of compositions of 7*n-5 into parts 6 and 7.
0, 0, 0, 0, 1, 6, 21, 56, 126, 252, 463, 805, 1378, 2457, 4823, 10556, 24753, 58976, 137808, 310974, 675850, 1420916, 2914906, 5900631, 11931283, 24360194, 50559900, 106791426, 228638698, 492908713, 1062928750, 2281600816, 4862773227, 10287720750
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-5-6*k));
Formula
a(n) = A017847(7*n-5).
a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-5-6*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^5*(1-x)/((1-x)^7 - x^6).