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

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =11a(6) =31a(7) =71a(8) =145a(9) =289a(10) =601a(11) =1321a(12) =2979a(13) =6683a(14) =14743a(15) =32111a(16) =69697a(17) =151777a(18) =332113a(19) =728689a(20) =1598883a(21) =3503627a(22) =7668079a(23) =16774775a(24) =36704017a(25) =80343361a(26) =175916521a(27) =385196761a(28) =843365379a(29) =1846290395