A373907 Number of compositions of 7*n into parts 1 and 7.
1, 2, 10, 53, 264, 1294, 6349, 31200, 153366, 753836, 3705166, 18211117, 89508951, 439943336, 2162355196, 10628140702, 52238121106, 256754344524, 1261967164192, 6202664757387, 30486569842400, 149843813435961, 736493759087077, 3619922936674360
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (8,-21,35,-35,21,-7,1).
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+6*k, n-k));
Formula
a(n) = A005709(7*n).
a(n) = Sum_{k=0..n} binomial(n+6*k,n-k).
a(n) = 8*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: 1/(1 - x - x/(1 - x)^6).