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A373911
Number of compositions of 7*n into parts 5 and 7.
5
1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 794, 1732, 3553, 7116, 14501, 31078, 70607, 166922, 399315, 946121, 2197582, 4998597, 11188280, 24835641, 55117511, 123036293, 276976136, 628285812, 1431723937, 3265884047, 7436635822, 16880558594, 38196652951, 86238054374
OFFSET
0,6
FORMULA
a(n) = A369816(7*n).
a(n) = Sum_{k=0..floor(n/5)} binomial(n+2*k,n-5*k).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 22*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: 1/(1 - x - x^5/(1 - x)^6).
MATHEMATICA
LinearRecurrence[{7, -21, 35, -35, 22, -7, 1}, {1, 1, 1, 1, 1, 2, 9}, 40] (* Harvey P. Dale, Oct 19 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\5, binomial(n+2*k, n-5*k));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 22 2024
STATUS
approved