a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026725.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =13a(5) =23a(6) =57a(7) =103a(8) =249a(9) =455a(10) =1083a(11) =1993a(12) =4693a(13) =8679a(14) =20275a(15) =37633a(16) =87377a(17) =162643a(18) =375789a(19) =701075a(20) =1613413a(21) =3015563a(22) =6916957a(23) =12948083a(24) =29617161a(25) =55513327a(26) =126678893a(27) =237705547a(28) =541325021a(29) =1016736115