"Rounded hypotenuses": a(n) = round(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) =8a(7) =10a(8) =13a(9) =16a(10) =21a(11) =26a(12) =33a(13) =42a(14) =53a(15) =68a(16) =86a(17) =110a(18) =140a(19) =178a(20) =226a(21) =288a(22) =366a(23) =466a(24) =593a(25) =754a(26) =959a(27) =1220a(28) =1552a(29) =1974