a(n) = Sum_{i=0..floor(n/2)} T(2i,n-2i), array T as in A049723.

Terms

a(0) =1a(1) =4a(2) =18a(3) =31a(4) =73a(5) =105a(6) =204a(7) =249a(8) =412a(9) =501a(10) =760a(11) =865a(12) =1207a(13) =1376a(14) =1864a(15) =2070a(16) =2688a(17) =2951a(18) =3740a(19) =4068a(20) =5059a(21) =5413a(22) =6612a(23) =7057a(24) =8421a(25) =8974a(26) =10620a(27) =11247a(28) =13114a(29) =13835