a(n) = floor(sqrt(F(n+2)^2 + F(n)^2)), where F(n) = A000045(n).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =8a(5) =13a(6) =22a(7) =36a(8) =58a(9) =95a(10) =154a(11) =249a(12) =403a(13) =652a(14) =1056a(15) =1709a(16) =2766a(17) =4475a(18) =7241a(19) =11717a(20) =18959a(21) =30676a(22) =49635a(23) =80311a(24) =129947a(25) =210258a(26) =340205a(27) =550464a(28) =890670a(29) =1441135