1/4 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having distinct edge sums.

Terms

a(0) =8a(1) =17a(2) =34a(3) =80a(4) =170a(5) =410a(6) =882a(7) =2138a(8) =4610a(9) =11186a(10) =24130a(11) =58562a(12) =126338a(13) =306626a(14) =661506a(15) =1605506a(16) =3463682a(17) =8406530a(18) =18136066a(19) =44017154a(20) =94961666a(21) =230476802a(22) =497225730a(23) =1206792194a(24) =2603507714a(25) =6318845954a(26) =13632143362a(27) =33085906946a(28) =71378829314