Floor-Sqrt transform of Catalan numbers (A000108).

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =11a(7) =20a(8) =37a(9) =69a(10) =129a(11) =242a(12) =456a(13) =861a(14) =1635a(15) =3113a(16) =5946a(17) =11386a(18) =21854a(19) =42038a(20) =81019a(21) =156416a(22) =302460a(23) =585712a(24) =1135739a(25) =2204982a(26) =4285715a(27) =8338678a(28) =16240318a(29) =31658209