a(n) = Sum_{i=0..floor(n/2)} T(2i,n-2i), array T as in A048149.

Terms

a(0) =1a(1) =3a(2) =12a(3) =19a(4) =43a(5) =60a(6) =114a(7) =138a(8) =225a(9) =271a(10) =408a(11) =462a(12) =641a(13) =728a(14) =982a(15) =1087a(16) =1407a(17) =1542a(18) =1948a(19) =2115a(20) =2625a(21) =2805a(22) =3420a(23) =3646a(24) =4343a(25) =4624a(26) =5464a(27) =5783a(28) =6735a(29) =7100