a(n) = Sum_{i=0..n} T(i,n-i), array T as in A049639.

Terms

a(0) =0a(1) =0a(2) =2a(3) =4a(4) =7a(5) =10a(6) =15a(7) =20a(8) =27a(9) =34a(10) =45a(11) =56a(12) =69a(13) =82a(14) =101a(15) =120a(16) =143a(17) =166a(18) =195a(19) =224a(20) =257a(21) =290a(22) =333a(23) =376a(24) =423a(25) =470a(26) =529a(27) =588a(28) =653a(29) =718