T(n,k)=Number of n X n 0..k matrices with each 2X2 subblock idempotent.

Terms

a(0) =2a(1) =3a(2) =8a(3) =4a(4) =12a(5) =32a(6) =5a(7) =16a(8) =50a(9) =78a(10) =6a(11) =20a(12) =72a(13) =108a(14) =196a(15) =7a(16) =24a(17) =98a(18) =142a(19) =260a(20) =428a(21) =8a(22) =28a(23) =128a(24) =180a(25) =332a(26) =542a(27) =916a(28) =9a(29) =32