1/4 the number of (n+1) X 3 binary arrays with all 2 X 2 subblock sums the same.

Terms

a(0) =6a(1) =8a(2) =11a(3) =17a(4) =27a(5) =47a(6) =83a(7) =155a(8) =291a(9) =563a(10) =1091a(11) =2147a(12) =4227a(13) =8387a(14) =16643a(15) =33155a(16) =66051a(17) =131843a(18) =263171a(19) =525827a(20) =1050627a(21) =2100227a(22) =4198403a(23) =8394755a(24) =16785411a(25) =33566723a(26) =67125251a(27) =134242307a(28) =268468227a(29) =536920067