"Ceiling of hypotenuses": a(n) = ceiling(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.

Terms

a(0) =1a(1) =3a(2) =4a(3) =5a(4) =7a(5) =9a(6) =12a(7) =15a(8) =20a(9) =25a(10) =33a(11) =42a(12) =54a(13) =69a(14) =88a(15) =112a(16) =143a(17) =182a(18) =232a(19) =295a(20) =376a(21) =478a(22) =609a(23) =775a(24) =986a(25) =1255a(26) =1597a(27) =2032a(28) =2585a(29) =3289