a(n) = Sum_{k=0..n} C(n,floor(k/2))*(-4)^(n-k).

Terms

a(0) =1a(1) =-3a(2) =14a(3) =-57a(4) =246a(5) =-1038a(6) =4424a(7) =-18777a(8) =79846a(9) =-339258a(10) =1442004a(11) =-6128202a(12) =26045436a(13) =-110691948a(14) =470442924a(15) =-1999378137a(16) =8497365126a(17) =-36113785698a(18) =153483619604a(19) =-652305322542