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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. 2

%I

%S 0,0,1,1,0,0,3,10,0,0,76,140,0,0,2478,5454,0,0,105704,267312,0,0,

%T 7235244,25244832,0,0,709868768,2310292004,0,0,91242419796,

%U 339602328050,0,0,15469115987732,54988746724416,0,0,3075508960864496,11965953308933012

%N 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 The variant was devised by Bernardo Recamán Santos and Freddy Barrera in Bogotá, who calculated up to a(20).

%C 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 Edward Moody, <a href="/A336747/b336747.txt">Table of n, a(n) for n = 1..66</a>

%H J. E. Miller, <a href="http://dialectrix.com/langford/ColombianVariant.html">Colombian Variant of Langford's Problem</a>

%H Edward Moody, <a href="https://github.com/EdwardMGraphite/colombian-langford">Java program for enumerating Colombian Langford pairings</a>

%e The unique Langford pairings for n=3 and n=4 are also Colombian:

%e 3 1 2 1 3 2 and 4 1 3 1 2 4 3 2.

%e For n=7, the a(7)=3 solutions are:

%e 4 1 6 1 7 4 3 5 2 6 3 2 7 5,

%e 2 3 6 2 7 3 4 5 1 6 1 4 7 5,

%e 7 3 1 6 1 3 4 5 7 2 6 4 2 5.

%Y Cf. A014552, A336861.

%K nonn

%O 1,7

%A _Edward Moody_, Aug 02 2020

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Last modified August 14 05:20 EDT 2022. Contains 356110 sequences. (Running on oeis4.)