a(n) = 2^n+(1+(n mod 2)/2)*C(n+1,floor((n+(n mod 2))/2))-1.

Terms

a(0) =1a(1) =4a(2) =6a(3) =16a(4) =25a(5) =61a(6) =98a(7) =232a(8) =381a(9) =889a(10) =1485a(11) =3433a(12) =5811a(13) =13339a(14) =22818a(15) =52072a(16) =89845a(17) =204001a(18) =354521a(19) =801421a(20) =1401291a(21) =3155299a(22) =5546381a(23) =12444841a(24) =21977515a(25) =49155331a(26) =87167163a(27) =194392627a(28) =345994215a(29) =769547191