Sum k=0..n, C(n-k, floor(k/2))4^k.

Terms

a(0) =1a(1) =5a(2) =5a(3) =21a(4) =101a(5) =181a(6) =517a(7) =2133a(8) =5029a(9) =13301a(10) =47429a(11) =127893a(12) =340709a(13) =1099573a(14) =3145861a(15) =8597205a(16) =26190373a(17) =76524149a(18) =214079429a(19) =633125397a(20) =1857511781a(21) =5282782645a(22) =15412788997a(23) =45132977493a(24) =129657499813a(25) =376262123765