a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026725.

Terms

a(0) =1a(1) =3a(2) =7a(3) =16a(4) =34a(5) =74a(6) =154a(7) =330a(8) =682a(9) =1451a(10) =2989a(11) =6332a(12) =13018a(13) =27495a(14) =56449a(15) =118954a(16) =243964a(17) =513180a(18) =1051612a(19) =2208856a(20) =4523344a(21) =9489604a(22) =19422124a(23) =40704746a(24) =83269990a(25) =174366100a(26) =356558320a(27) =746073604a(28) =1525104172a(29) =3189119418