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 A346757 #25 Sep 29 2021 10:55:19 %S A346757 0,2,2,12,20,88,180,716,1648,6244,15512,57188,149892,543324,1481636, %T A346757 5310764,4930380,53102508,152935148,540918660,1588618212,5595773136, %U A346757 16701973552 %N A346757 a(n) is the number of arches with a length of one and exactly one covering arch for semi-meanders with n top arches. %C A346757 The ratio of the number of semi-meanders in generation n+1 to the number of semi-meanders in generation n is equal to the ratio of the differences of these semi-meander subset arch sequences in successive generations. %C A346757 A000682(n+1)/A000682(n) = (A260785(n+3) - a(n+1))/(A260785(n+2) - a(n)). %D A346757 See A000682. %H A346757 P. Di Francesco, O. Golinelli and E. Guitter, <a href="https://arxiv.org/abs/cond-mat/9910453">Meanders: exact asymptotics</a>, arXiv:cond-mat/9910453 [cond-mat.stat-mech], 1999-2000; Nuclear Physics B, volume 570, issue 3, 27 March 2000, 699-712. %F A346757 For n >= 2, a(n) = A260785(n+2) - 2*A000682(n). %e A346757 n = 5, || indicates an arch of length one with exactly one covering arch. %e A346757 /\ /\ /\ %e A346757 /\ //\\ //\\ /\ /\ /\ /\ /\ / \ %e A346757 //\\ ///\\\ ///\\\ //\\ /\ //\\ //\\ //\\ //\\ /\ /\ /\ //\/\\ %e A346757 || || || || || || |||| %e A346757 /\ /\ %e A346757 / \ / \ /\ %e A346757 //\ \ / /\\ / \ %e A346757 ///\\/\\ /\ /\ //\//\\\ //\/\\ /\ /\ %e A346757 || || |||| a(5) = 12. %Y A346757 Cf. A000682, A260785. %K A346757 nonn,more %O A346757 2,2 %A A346757 _Roger Ford_, Aug 01 2021