A373936 Number of compositions of 7*n-4 into parts 6 and 7.
0, 0, 0, 1, 5, 15, 35, 70, 126, 211, 342, 573, 1079, 2366, 5733, 14197, 34223, 78832, 173166, 364876, 745066, 1493990, 2985725, 6030652, 12428911, 26199706, 56231526, 121847272, 264270015, 570020037, 1218672066, 2581172411, 5424947523, 11347651254
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-4-6*k));
Formula
a(n) = A017847(7*n-4).
a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-4-6*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^4*(1-x)^2/((1-x)^7 - x^6).