a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=n, T given by A026681.

Terms

a(0) =1a(1) =3a(2) =8a(3) =20a(4) =46a(5) =100a(6) =220a(7) =496a(8) =1102a(9) =2390a(10) =5242a(11) =11726a(12) =25982a(13) =56524a(14) =124092a(15) =276898a(16) =613052a(17) =1336324a(18) =2935674a(19) =6541128a(20) =14475308a(21) =31594190a(22) =69437408a(23) =154561826a(24) =341929544a(25) =747004042a(26) =1642277456a(27) =3652837124a(28) =8079030958