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A336747 Number of Colombian variant Langford pairings (solutions to Langford problem such that exactly one instance of {1, 2, 3, ..., n-2, n} occurs between the two instances of n-1), up to reversal of the order.

%I A336747 #27 Sep 05 2020 07:00:47
%S A336747 0,0,1,1,0,0,3,10,0,0,76,140,0,0,2478,5454,0,0,105704,267312,0,0,
%T A336747 7235244,25244832,0,0,709868768,2310292004,0,0,91242419796,
%U A336747 339602328050,0,0,15469115987732,54988746724416,0,0,3075508960864496,11965953308933012
%N A336747 Number of Colombian variant Langford pairings (solutions to Langford problem such that exactly one instance of {1, 2, 3, ..., n-2, n} occurs between the two instances of n-1), up to reversal of the order.
%C A336747 The variant was devised by Bernardo Recamán Santos and Freddy Barrera in Bogotá, who calculated up to a(20).
%C A336747 Ceiling((n-1-sqrt(n+1))/2) is a lower bound for the number of items outside the instance of n-1 at one end, e.g. for n=7 there are at least two items before the first '6'. This bound is tight until at least n=184.
%H A336747 Edward Moody, <a href="/A336747/b336747.txt">Table of n, a(n) for n = 1..66</a>
%H A336747 J. E. Miller, <a href="http://dialectrix.com/langford/ColombianVariant.html">Colombian Variant of Langford's Problem</a>
%H A336747 Edward Moody, <a href="https://github.com/EdwardMGraphite/colombian-langford">Java program for enumerating Colombian Langford pairings</a>
%e A336747 The unique Langford pairings for n=3 and n=4 are also Colombian:
%e A336747   3 1 2 1 3 2 and 4 1 3 1 2 4 3 2.
%e A336747 For n=7, the a(7)=3 solutions are:
%e A336747   4 1 6 1 7 4 3 5 2 6 3 2 7 5,
%e A336747   2 3 6 2 7 3 4 5 1 6 1 4 7 5,
%e A336747   7 3 1 6 1 3 4 5 7 2 6 4 2 5.
%Y A336747 Cf. A014552, A336861.
%K A336747 nonn
%O A336747 1,7
%A A336747 _Edward Moody_, Aug 02 2020