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 A298122 #26 Jan 14 2018 16:57:32 %S A298122 1,1,2,5,11,34,90,300,875,3038,9408,33516,108108,392040,1302444, %T A298122 4785066,16256955,60324550,208579800,780088452,2735682092,10296854984, %U A298122 36532677272,138231751840,495241833996,1882201158264,6799413051200,25939319270000,94374970110000 %N A298122 a(n) is the number of n nonintersecting arches above the x-axis that start and/or end with an arch length equal to one and have floor((n+2)/2) arches starting in odd numbered positions. %F A298122 a(1) = a(2) = 1, a(3) = 2; for n > 3, a(n) = 2*(C(n-1, floor((n-1)/2))*C(n-2, floor((n-2)/2)) - (C(n-1, floor((n-2)/2))*C(n-2, floor((n-3)/2)))) - (C(n-3, floor((n-1)/2))*C(n-2, floor((n-1)/2))/(floor((n-1)/2)+1)). %e A298122 Example: For n = 4 the a(4) = 5 solutions are as follows. (The numbers under the arches represent arches starting in an odd-numbered position on the x-axis.) %e A298122 /\ /\ %e A298122 //\\ /\ /\ //\\ /\ %e A298122 ///\\\/\, //\\ /\ /\, /\//\\/\, /\///\\\, /\/\//\\. %e A298122 1 3 7 1 5 7 1 3 7 1 3 5 1 3 5 %Y A298122 Cf. A001263, A005558. %K A298122 nonn %O A298122 1,3 %A A298122 _Roger Ford_, Jan 12 2018