Squares and omitting some digit gives another number in this list.

Terms

a(0) =0a(1) =1a(2) =4a(3) =9a(4) =16a(5) =49a(6) =64a(7) =81a(8) =100a(9) =169a(10) =196a(11) =400a(12) =841a(13) =900a(14) =1296a(15) =1369a(16) =1600a(17) =1936a(18) =4900a(19) =6400a(20) =8100a(21) =10000a(22) =12996a(23) =13689a(24) =16900a(25) =19600a(26) =40000a(27) =64009a(28) =84100a(29) =90000