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A336747
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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.
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2
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0, 0, 1, 1, 0, 0, 3, 10, 0, 0, 76, 140, 0, 0, 2478, 5454, 0, 0, 105704, 267312, 0, 0, 7235244, 25244832, 0, 0, 709868768, 2310292004, 0, 0, 91242419796, 339602328050, 0, 0, 15469115987732, 54988746724416, 0, 0, 3075508960864496, 11965953308933012
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OFFSET
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1,7
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COMMENTS
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The variant was devised by Bernardo Recamán Santos and Freddy Barrera in Bogotá, who calculated up to a(20).
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.
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LINKS
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Edward Moody, Table of n, a(n) for n = 1..66
J. E. Miller, Colombian Variant of Langford's Problem
Edward Moody, Java program for enumerating Colombian Langford pairings
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EXAMPLE
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The unique Langford pairings for n=3 and n=4 are also Colombian:
3 1 2 1 3 2 and 4 1 3 1 2 4 3 2.
For n=7, the a(7)=3 solutions are:
4 1 6 1 7 4 3 5 2 6 3 2 7 5,
2 3 6 2 7 3 4 5 1 6 1 4 7 5,
7 3 1 6 1 3 4 5 7 2 6 4 2 5.
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CROSSREFS
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Cf. A014552, A336861.
Sequence in context: A113116 A137044 A188545 * A212361 A011998 A278759
Adjacent sequences: A336744 A336745 A336746 * A336748 A336749 A336750
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KEYWORD
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nonn
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AUTHOR
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Edward Moody, Aug 02 2020
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STATUS
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approved
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