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 A141110 #17 Dec 27 2021 08:26:38 %S A141110 1,1,1,2,1,1,3,2,1,3,1,2,3,1,3,4,3,1,3,2,3,5,1,2,5,1,3,4,1,1,7,6,1,3, %T A141110 1,4,5,3,1,4,1,7,3,4,5,7,3,2,7,1,1,8,1,3,3,4,3,7,5,2,5,3,9,10,1,5,7,2, %U A141110 1,3,3,6,5,1,5,8,7,3,3,4,1,9,1,2,11 %N A141110 Number of cycles and fixed points in the permutation (n, n-2, n-4, ..., 1, ..., n-3, n-1). %C A141110 The above permutation (see A130517) can be generated by taking S_n: (1, 2, ..., n) and reversing the first two, first three and so on till first n, elements in sequence. Interestingly this permutation orbit has length given by A003558. %H A141110 T. D. Noe, <a href="/A141110/b141110.txt">Table of n, a(n) for n = 1..10000</a> %e A141110 a(20) = 2, since (20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19) has two cycles (1, 20, 19, 17, 13, 5, 12, 3, 16, 11) and (2, 18, 15, 9, 4, 14, 7, 8, 6, 10). %o A141110 (Python) %o A141110 from sympy.combinatorics import Permutation %o A141110 def a(n): %o A141110 p = list(range(n, 0, -2)) + list(range(1+(n%2), n, 2)) %o A141110 return Permutation([pi-1 for pi in p]).cycles %o A141110 print([a(n) for n in range(1, 86)]) # _Michael S. Branicky_, Dec 27 2021 %Y A141110 Cf. A130517 (permutations), A003558 (order). %K A141110 easy,nonn %O A141110 1,4 %A A141110 _Ramasamy Chandramouli_, Jun 05 2008