a(n) = Sum_{i=0..floor(n/2)} T(2i+1,n-2i-1) where T is A049627.

Terms

a(0) =0a(1) =2a(2) =4a(3) =7a(4) =12a(5) =17a(6) =26a(7) =34a(8) =50a(9) =61a(10) =84a(11) =100a(12) =132a(13) =154a(14) =198a(15) =224a(16) =280a(17) =314a(18) =384a(19) =427a(20) =514a(21) =563a(22) =666a(23) =726a(24) =848a(25) =918a(26) =1062a(27) =1141a(28) =1306a(29) =1399