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 A383857 #16 May 24 2025 21:48:41 %S A383857 0,0,2,8,34,196,1366,10928,98330,983036,10811134,129714184,1686103522, %T A383857 23603603540,354033474374,5664286296416,96289603698346, %U A383857 1733166940314028,32929480177913230,658578501071986616,13829959293448920434,304255691156335505924 %N A383857 Number of permutations of [n] such that precisely one rising or falling succession occurs, but without either n(n-1) or (n-1)n. %C A383857 See A086852 or 2*A000130 for the counting including the successions n(n-1) and (n-1)n. See also the k = 1 columns of the triangles A001100 and 2*A086856. %C A383857 For the number of permutations of length n without rising or falling successions see A002464(n). %F A383857 a(n) = A002464(n+1) - (n-1) * A002464(n). %e A383857 a(3) = 2*1 from the permutations 213 and the reverted 312. %e A383857 a(4) = 2*4 from 1324, 1423, 2314, 3124 and the reverted 4231, 3241, 4132, 4213. %e A383857 a(5) = 2*17 from the permutations corresponding to A086852(5) = 2*20, without 13542, 24513, 25413, and the reverted 24531, 31542, 31452. %Y A383857 Cf. A000130, A001100, A002464, A086852, A086856. %K A383857 nonn,easy %O A383857 1,3 %A A383857 _Wolfdieter Lang_, May 19 2025