a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.

Terms

a(0) =1a(1) =3a(2) =3a(3) =4a(4) =5a(5) =6a(6) =7a(7) =9a(8) =11a(9) =14a(10) =17a(11) =22a(12) =27a(13) =34a(14) =43a(15) =54a(16) =69a(17) =87a(18) =111a(19) =141a(20) =179a(21) =227a(22) =289a(23) =367a(24) =467a(25) =593a(26) =754a(27) =959a(28) =1219a(29) =1551