This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080972 #8 Jan 10 2024 16:35:12 %S A080972 1,1,1,2,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,2,1,1,1,1,1,1,1,1, %T A080972 2,1,1,2,1,1,2,1,1,2,1,2,3,1,2,1,4,1,2,1,2,2,3,3,1,2,2,1,2,4,1,1,2,1, %U A080972 4,4,1,2,2,1,2,4,1,2,4,2,4,1,1,4,4,1,4,1,2,1,4,4,2,1,4,4,2,4,4,2,1 %N A080972 a(n) = A080969(n)/A080967(A080979(A080970(n))). %C A080972 Donaghey shows in his paper that the orbit size (under the automorphism A057505/A057506) of each non-branch-reduced tree encoded by A080971(n) is divisible by the orbit size of the corresponding branch-reduced tree. This sequence gives the corresponding ratio. %H A080972 Robert Donaghey, <a href="https://doi.org/10.1016/0095-8956(80)90045-3">Automorphisms on Catalan trees and bracketing</a>, J. Combin. Theory, Series B, 29 (1980), 75-90. %K A080972 nonn %O A080972 0,4 %A A080972 _Antti Karttunen_, Mar 02 2003