Number of ordered subsequences of {1,...,2n} containing at least n elements and such that the first differences contain only odd numbers.
(history;
published version)
a(n) ~ c * (27/4)^(n/2) / sqrt(3*Pi*n/2), where c = 14 if n is even and c = 8*sqrt(3) if n is odd. Equivalently, c = 7 + 4*sqrt(3) + (7 - 4*sqrt(3))*(-1)^n. - Vaclav Kotesovec, Jun 19 2021