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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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.

LINKS

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

EXAMPLE

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.

CROSSREFS

Cf. A014552, A336861.

Sequence in context: A113116 A137044 A188545 * A212361 A011998 A278759

Adjacent sequences:  A336744 A336745 A336746 * A336748 A336749 A336750

KEYWORD

nonn

AUTHOR

Edward Moody, Aug 02 2020

STATUS

approved

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Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)