OFFSET
0,6
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,22,-7,1).
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