OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (2 * a(n-1) + n * a(n-3) + 1)/3 for n > 2.
a(n) ~ c * n^(n/3 + 1/2) / (3^(n/3) * exp(n/3 - n^(2/3)/3^(2/3) - 2*n^(1/3) / 3^(7/3))) * (1 + 1235/(729 * 3^(2/3) * n^(1/3)) + 9452027/(15943230 * 3^(1/3) * n^(2/3)) + 16015315669/(41841412812*n)), where c = 0.50682110703119..., conjecture: c = exp(4/81) * sqrt(2*Pi) / 3^(3/2). - Vaclav Kotesovec, Nov 25 2022
PROG
(PARI) a(n) = sum(k=0, n\3, (n-2*k)!/(n-3*k)!);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 19 2022
STATUS
approved