a(n) = Sum_{i=0..floor(n/2)} T(2i,n-2i) where T is A049627.

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =10a(5) =17a(6) =22a(7) =34a(8) =42a(9) =61a(10) =72a(11) =100a(12) =116a(13) =154a(14) =176a(15) =224a(16) =250a(17) =314a(18) =348a(19) =427a(20) =470a(21) =563a(22) =612a(23) =726a(24) =786a(25) =918a(26) =988a(27) =1141a(28) =1220a(29) =1399