a(n) = Sum_{j=0..n} Sum_{i=0..n} T(j,i), T given by A026736.

Terms

a(0) =1a(1) =3a(2) =7a(3) =15a(4) =32a(5) =66a(6) =139a(7) =285a(8) =599a(9) =1227a(10) =2577a(11) =5277a(12) =11075a(13) =22671a(14) =47543a(15) =97287a(16) =203860a(17) =417006a(18) =873175a(19) =1785513a(20) =3736210a(21) =7637604a(22) =15972143a(23) =32641221a(24) =68224004a(25) =139389570a(26) =291199307a(27) =594818781a(28) =1242097912a(29) =2536656174