OFFSET
0,4
COMMENTS
Number of compositions of 7*n-2 into parts 2 and 7.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-20,35,-35,21,-7,1).
FORMULA
a(n) = A369813(7*n-2) for n > 0.
a(n) = 7*a(n-1) - 20*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.
a(n) = Sum_{k=0..floor(n/2)} binomial(n-1+5*k,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^7))
(PARI) a(n) = sum(k=0, n\2, binomial(n-1+5*k, n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2024
STATUS
approved