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 A085159 #9 Oct 15 2015 10:55:24 %S A085159 0,1,2,3,4,6,7,5,8,9,11,14,16,19,17,20,12,10,13,21,15,18,22,23,25,28, %T A085159 30,33,37,39,42,44,47,51,53,56,60,45,48,54,57,61,31,34,26,24,27,35,29, %U A085159 32,36,58,62,40,38,41,49,43,46,50,63,52,55,59,64,65,67,70,72,75 %N A085159 Permutation of natural numbers induced by the Catalan bijection gma085159 acting on symbolless S-expressions encoded by A014486/A063171. %C A085159 This Catalan bijection rotates the interpretations (pp)-(rr) of Stanley, using the "rising slope" mapping illustrated in A085161. %H A085159 A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (With the complete Scheme source) %H A085159 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations induced by Catalan automorphisms</a> %H A085159 R. P. Stanley, <a href="http://www-math.mit.edu/~rstan/ec/catalan.pdf">Exercises on Catalan and Related Numbers</a> (including 66 combinatorial interpretations) %o A085159 (Scheme functions implementing this automorphism on list-structures:) %o A085159 (define (gma085159 s) (cond ((null? s) s) (else (app-to-xrt (car s) (append (cdr s) (list (list))))))) %Y A085159 Inverse: A085160. a(n) = A085161(A085160(A085161(n))) = A085169(A082315(A085170(n))) = A074684(A082315(A074683(n))) = A085173(A085173(n)). Occurs in A073200. Cf. also A085165-A085168, A086429. Scheme-function app-to-xrt given in A085203. %Y A085159 Number of cycles: A054357. Number of fixed points: A046698. (In range [A014137(n-1)..A014138(n-1)] of this permutation, possibly shifted one term left or right). %K A085159 nonn %O A085159 0,3 %A A085159 _Antti Karttunen_, Jun 23 2003