Number of (n+1) X 3 0..1 matrices with each 2 X 2 subblock idempotent.

Terms

a(0) =16a(1) =32a(2) =52a(3) =86a(4) =137a(5) =218a(6) =345a(7) =547a(8) =869a(9) =1385a(10) =2214a(11) =3549a(12) =5702a(13) =9178a(14) =14794a(15) =23872a(16) =38551a(17) =62292a(18) =100695a(19) =162821a(20) =263331a(21) =425947a(22) =689052a(23) =1114751a(24) =1803532a(25) =2917988a(26) =4721200a(27) =7638842a(28) =12359669a(29) =19998110