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

Terms

a(0) =122a(1) =178a(2) =297a(3) =416a(4) =628a(5) =1045a(6) =1694a(7) =2668a(8) =4265a(9) =6922a(10) =11196a(11) =18035a(12) =29122a(13) =47134a(14) =76253a(15) =123292a(16) =199424a(17) =322681a(18) =522090a(19) =844664a(20) =1366621a(21) =2211238a(22) =3577832a(23) =5788951a(24) =9366638a(25) =15155530a(26) =24522129a(27) =39677528a(28) =64199500a(29) =103876957