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A373907
Number of compositions of 7*n into parts 1 and 7.
12
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
0,2
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).
PROG
(PARI) a(n) = sum(k=0, n, binomial(n+6*k, n-k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 22 2024
STATUS
approved