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 A127377 #6 Mar 31 2012 13:21:14 %S A127377 0,1,3,2,8,7,6,4,5,22,21,20,17,18,14,15,19,9,10,16,11,13,12,64,63,62, %T A127377 58,59,54,55,61,45,46,57,48,50,49,37,38,39,41,40,51,52,60,23,24,56,25, %U A127377 27,26,42,43,53,28,29,44,33,36,35,47,30,34,31,32,196,195,194,189,190 %N A127377 Signature-permutation of a Catalan automorphism, auxiliary bijection for Callan's 2006 bijection on Dyck Paths. %C A127377 Used to construct A127379. %H A127377 A. Karttunen, <a href="/A127377/b127377.txt">Table of n, a(n) for n = 0..2055</a> %H A127377 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a> %o A127377 (Scheme implementation of this automorphism, destructive, that acts on S-expressions, i.e. list-structures:) %o A127377 (define (*A127377! s) (cond ((null? s)) ((null? (car s)) (*A069770! s) (*A127377! (car s))) ((null? (cdr s)) (*A069770! s) (*A127379! (cdr s))) (else (*A127379! s))) s) %Y A127377 Inverse: A127378. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A127383 and A127389. The maximum cycles and LCM's of cycle sizes begin as 1, 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16, 16, ... A127387 shows a variant which is an involution. A127302(a(n)) = A127302(n) holds for all n. %K A127377 nonn %O A127377 0,3 %A A127377 _Antti Karttunen_, Jan 16 2007