a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026758.

Terms

a(0) =1a(1) =3a(2) =7a(3) =16a(4) =34a(5) =75a(6) =157a(7) =345a(8) =721a(9) =1588a(10) =3322a(11) =7342a(12) =15382a(13) =34117a(14) =71587a(15) =159322a(16) =334792a(17) =747507a(18) =1572937a(19) =3522561a(20) =7421809a(21) =16667530a(22) =35158972a(23) =79162689a(24) =167170123a(25) =377291856a(26) =797535322a(27) =1803925336a(28) =3816705364