a(n) = Sum_{i=0..floor(n/2)} T(2i,n-2i), array T as in A049747.

Terms

a(0) =0a(1) =2a(2) =6a(3) =10a(4) =23a(5) =33a(6) =60a(7) =74a(8) =121a(9) =147a(10) =218a(11) =256a(12) =349a(13) =407a(14) =552a(15) =612a(16) =785a(17) =875a(18) =1094a(19) =1210a(20) =1501a(21) =1603a(22) =1948a(23) =2088a(24) =2503a(25) =2677a(26) =3146a(27) =3344a(28) =3891a(29) =4125