a(n) = 4^n*(n/4 + binomial(n+1/2, 1/2)).

Terms

a(0) =1a(1) =7a(2) =38a(3) =188a(4) =886a(5) =4052a(6) =18156a(7) =80152a(8) =349862a(9) =1513604a(10) =6501316a(11) =27759272a(12) =117935548a(13) =498920008a(14) =2102905496a(15) =8835174960a(16) =37015522054a(17) =154690661732a(18) =645017651412