a(n) = Sum_{k=0..floor(n/2)} binomial(k+2,4*n-8*k+2).

Terms

a(0) =1a(1) =0a(2) =3a(3) =0a(4) =6a(5) =0a(6) =10a(7) =0a(8) =15a(9) =1a(10) =21a(11) =7a(12) =28a(13) =28a(14) =36a(15) =84a(16) =45a(17) =210a(18) =56a(19) =462a(20) =77a(21) =924a(22) =144a(23) =1716a(24) =377a(25) =3003a(26) =1106a(27) =5006a(28) =3123a(29) =8023