1/4 the number of (n+1) X 2 binary arrays with all 2 X 2 subblock sums the same.

Terms

a(0) =4a(1) =6a(2) =9a(3) =15a(4) =25a(5) =45a(6) =81a(7) =153a(8) =289a(9) =561a(10) =1089a(11) =2145a(12) =4225a(13) =8385a(14) =16641a(15) =33153a(16) =66049a(17) =131841a(18) =263169a(19) =525825a(20) =1050625a(21) =2100225a(22) =4198401a(23) =8394753a(24) =16785409a(25) =33566721a(26) =67125249a(27) =134242305a(28) =268468225a(29) =536920065