Floor-Sqrt transform of Motzkin numbers (A001006).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =4a(6) =7a(7) =11a(8) =17a(9) =28a(10) =46a(11) =76a(12) =124a(13) =204a(14) =337a(15) =557a(16) =923a(17) =1535a(18) =2556a(19) =4266a(20) =7131a(21) =11939a(22) =20019a(23) =33611a(24) =56504a(25) =95096a(26) =160218a(27) =270199a(28) =456095a(29) =770547