A204575 Squares such that [a(n)/2] is again a square (A055792), written in binary.
0, 1, 1001, 100100001, 10011001001001, 1010001010010000001, 101011001001001011001001, 10110111001100110101000100001, 1100001001111011011000010110001001, 110011100111010101001010101001000000001
Offset: 1