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 A154456 #4 Mar 31 2012 13:21:18 %S A154456 0,1,3,2,7,8,6,4,5,17,18,20,22,21,16,19,14,9,10,15,11,12,13,45,46,48, %T A154456 49,50,54,55,61,63,64,57,62,58,59,44,47,53,60,56,42,51,37,23,24,38,25, %U A154456 26,27,43,52,39,28,29,40,30,31,32,41,33,34,35,36,129,130,132,133,134 %N A154456 Signature permutation of a Catalan bijection: The inverse of A154455. %C A154456 This automorphism of rooted plane binary trees switches the two descendant trees for every other vertex as it descends along the 000... ray, starting swapping already at the root. Specifically, *A154456 = psi(A154446), where the isomorphism psi is given in A153141 (see further comments there). %H A154456 A. Karttunen, <a href="/A154456/b154456.txt">Table of n, a(n) for n = 0..2055</a> %H A154456 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a> %o A154456 (Scheme function, destructive implementation of this automorphism acting on S-expressions:) (define (*A154456! s) (cond ((pair? s) (*A069770! s) (*A154454! (car s)))) s) %Y A154456 Inverse: A154455. a(n) = A069768(A154450(n)) = A057163(A154452(A057163(n))). Cf. A069770, A154454. %Y A154456 Differs from A082346 and A122328 for the first time at n=26, where a(26)=49, while A082346(26)=A122328(26)=50. Differs from A129611 for the first time at n=91, where a(91)=196, while A129611(91)=195. %K A154456 nonn %O A154456 0,3 %A A154456 _Antti Karttunen_, Jan 17 2009