OFFSET
0,4
COMMENTS
Number of compositions of 5*n-2 into parts 2 and 5.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-9,10,-5,1).
FORMULA
a(n) = A001687(5*n-1) for n > 0.
a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.
a(n) = Sum_{k=0..floor(n/2)} binomial(n-1+3*k,n-2*k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^5))
(PARI) a(n) = sum(k=0, n\2, binomial(n-1+3*k, n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2024
STATUS
approved