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 A130918 #12 Jul 24 2025 19:13:24 %S A130918 0,1,3,2,8,7,6,5,4,22,21,20,19,18,17,16,15,14,13,12,11,10,9,64,63,62, %T A130918 61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39, %U A130918 38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,196,195,194,193,192 %N A130918 Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order. %C A130918 In principle this involution is the signature permutation of yet another Catalan automorphism. However, the question remains what is the most "natural" way to create such an automorphism acting e.g. on S-expressions (i.e. rooted plane binary trees), which would produce this sequence as its signature permutation. %H A130918 A. Karttunen, <a href="/A130918/b130918.txt">Table of n, a(n) for n = 0..2055</a> %H A130918 A. Karttunen, <a href="https://oeis.org/wiki/Signature_permutations_of_Catalan_bijections">Signature permutations of Catalan bijections</a> %H A130918 <a href="/index/Per#IntegerPermutationCatAuto">Index entries for signature-permutations of Catalan automorphisms</a> %F A130918 a(0)=0, a(n) = A014138(A072643(n)-1) - A082853(n). %o A130918 (Scheme) (define (A130918 n) (if (zero? n) n (- (A014138 (- (A072643 n) 1)) (A082853 n)))) %Y A130918 Inverse: A130918. Cf. A054429, A057163. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130380 and A036987. %K A130918 nonn %O A130918 0,3 %A A130918 _Antti Karttunen_, Jun 11 2007