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

Terms

a(0) =25a(1) =50a(2) =76a(3) =123a(4) =191a(5) =300a(6) =470a(7) =741a(8) =1173a(9) =1866a(10) =2980a(11) =4775a(12) =7671a(13) =12348a(14) =19906a(15) =32125a(16) =51885a(17) =83846a(18) =135548a(19) =219191a(20) =354515a(21) =573460a(22) =927706a(23) =1500873a(24) =2428261a(25) =3928790a(26) =6356680a(27) =10285071a(28) =16641323a(29) =26925936