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

Terms

a(0) =1a(1) =3a(2) =14a(3) =68a(4) =326a(5) =1532a(6) =7068a(7) =32104a(8) =143942a(9) =638444a(10) =2806196a(11) =12239768a(12) =53035804a(13) =228504408a(14) =979640696a(15) =4181649360a(16) =17780949574a(17) =75348050252a(18) =318312780612