OFFSET
0,5
COMMENTS
Number of compositions of 7*n-3 into parts 3 and 7.
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-21,36,-35,21,-7,1).
FORMULA
a(n) = A369814(7*n-3) for n > 0.
a(n) = 7*a(n-1) - 21*a(n-2) + 36*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/3)} binomial(n-1+4*k,n-3*k).
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(1/(1-x^3/(1-x)^7))
(PARI) a(n) = sum(k=0, n\3, binomial(n-1+4*k, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2024
STATUS
approved