a(n) = Sum_{k=0..floor(n/2)} binomial(k+3,4*n-8*k+3).

Terms

a(0) =1a(1) =0a(2) =4a(3) =0a(4) =10a(5) =0a(6) =20a(7) =0a(8) =35a(9) =1a(10) =56a(11) =8a(12) =84a(13) =36a(14) =120a(15) =120a(16) =165a(17) =330a(18) =221a(19) =792a(20) =298a(21) =1716a(22) =442a(23) =3432a(24) =819a(25) =6435a(26) =1925a(27) =11441a(28) =5048a(29) =19464