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%I #35 Jun 09 2021 22:40:42
%S 0,0,1,0,0,0,0,4,0,0,16,40,0,0,194,274,0,0,2384,4719,0,0,31856,62124,
%T 0,0,426502,817717,0,0,5724640,10838471,0,0,75178742,142349245,0,0,
%U 977964587,1850941916,0,0
%N Number of planar Langford sequences.
%C Enumerates the Langford sequences (counted by A014552) that have the additional property that we can draw noncrossing lines to connect the two 1s, the two 2s, ..., the two ns. For example, the four solutions for n=8 are 8642752468357131, 8613175368425724, 5286235743681417, 7528623574368141.
%D D. E. Knuth, TAOCP, Vol. 4, in preparation.
%H John E. Miller, <a href="http://dialectrix.com/langford.html">Langford's Problem</a>
%H Edward Moody, <a href="https://github.com/EdwardMGraphite/planar-langford">Java program for enumerating planar Langford sequences</a>
%H Zan Pan, <a href="https://eprint.panzan.me/articles/langford.pdf">Conjectures on the number of Langford sequences</a>, (2021).
%Y Cf. A014552, A059106.
%K nonn,more
%O 1,8
%A _Don Knuth_, Feb 03 2007
%E a(31) from _Rory Molinari_, Feb 21 2018
%E a(32)-a(34) from _Rory Molinari_, Mar 10 2018
%E a(35) from _Rory Molinari_, May 02 2018
%E a(36)-a(42) from _Edward Moody_, Apr 02 2019