OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (4 * a(n-1) - a(n-2) + 2 * (2*n-3) * a(n-3))/3 for n > 2.
a(n) ~ c * 2^(2*n/3) * n^(n/3) / (3^(n/3) * exp(n/3 - 2^(1/3) * n^(2/3) / 3^(2/3) + n^(1/3) / (2^(4/3) * 3^(7/3)))) * (1 + 7795/(5832*6^(2/3)*n^(1/3)) + 135724109/(2040733440*6^(1/3)*n^(2/3)) - 5962064767253/(42845606719488*n)), where c = 0.46562048925..., conjecture: c = sqrt(2) * exp(-1/81) / 3. - Vaclav Kotesovec, Nov 25 2022
PROG
(PARI) a(n) = sum(k=0, n\3, (n-k)!/(k!*(n-3*k)!));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 22 2022
STATUS
approved