OFFSET
0,7
COMMENTS
Number of compositions of 7*n-5 into parts 5 and 7.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,22,-7,1).
FORMULA
a(n) = A369816(7*n-5) for n > 0.
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) for n > 7.
a(n) = Sum_{k=0..floor(n/5)} binomial(n-1+2*k,n-5*k).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^5/(1-x)^7))
(PARI) a(n) = sum(k=0, n\5, binomial(n-1+2*k, n-5*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2024
STATUS
approved