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 A337581 #12 Sep 08 2020 03:26:37 %S A337581 1,2,4,8,16,40,96,264,696,2016,5624,16840,48792,149512,445112,1387384, %T A337581 4215496,13312752,41097864,131146520,410045672,1319612232,4169110888, %U A337581 13511677040,43060097728,140383359392 %N A337581 a(n) is the number of semi-meanders with n top arches that have both an arch of length 1 adjacent to the center of the top arch configuration and an arch of length 1 starting or ending the top arch configuration. %C A337581 The number of semi-meanders with n top arches is A000682(n). The number of semi-meanders with n top arches that have a starting or ending arch of length 1 is 2*A000682(n-1). The number of semi-meanders with n top arches that have an arch adjacent to the center with length 1 is 2*A000682(n-1). %F A337581 For n >= 4: a(n) = 4*A000682(n-2). %e A337581 For n = 5: (10) is a starting or ending arch of length 1, [10] is an arch adjacent to the center with length 1, a(5) = 8. %e A337581 (10)101[10]100, 110[10]010(10), (10)1[10]11000, 11100[10]0(10), (10)111[10]000, %e A337581 111[10]000(10), (10)1[10]01100, 11001[10]0(10). %e A337581 /\ = arch with length 1, (10) = arches with length 1 at ends or adjacent to center %e A337581 /\ /\ /\ %e A337581 / \ / \ / \ %e A337581 / /\ \ / /\ \ /\ / \ %e A337581 1 10 0 1(10) 0(10) /\ /\ / /\ /\\ %e A337581 center| end (10) 10 1(10)100 %e A337581 end center| %Y A337581 Cf. A000682. %K A337581 nonn,more %O A337581 2,2 %A A337581 _Roger Ford_, Sep 01 2020