A373911 Number of compositions of 7*n into parts 5 and 7.
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
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,22,-7,1).
Programs
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Mathematica
LinearRecurrence[{7,-21,35,-35,22,-7,1},{1,1,1,1,1,2,9},40] (* Harvey P. Dale, Oct 19 2024 *) -
PARI
a(n) = sum(k=0, n\5, binomial(n+2*k, n-5*k));
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).