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

Terms

a(0) =12a(1) =25a(2) =41a(3) =70a(4) =115a(5) =189a(6) =308a(7) =501a(8) =813a(9) =1318a(10) =2135a(11) =3457a(12) =5596a(13) =9057a(14) =14657a(15) =23718a(16) =38379a(17) =62101a(18) =100484a(19) =162589a(20) =263077a(21) =425670a(22) =688751a(23) =1114425a(24) =1803180a(25) =2917609a(26) =4720793a(27) =7638406a(28) =12359203a(29) =19997613