A176127 The number of permutations of {1,2,...,n,1,2,...,n} with the property that there are k numbers between the two k's in the set for k=1,...,n.

0, 0, 2, 2, 0, 0, 52, 300, 0, 0, 35584, 216288, 0, 0, 79619280, 653443600, 0, 0, 513629782560, 5272675722400, 0, 0, 7598911885030976, 93690316113031872, 0, 0, 223367222197529806464, 3214766521218764786304, 0, 0

Offset

1,3

References

For references, see A014552.

Links

Table of n, a(n) for n=1..30.

Ali Assarpour, Amotz Bar-Noy, Ou Liuo, Counting the Number of Langford Skolem Pairings, arXiv:1507.00315 [cs.DM], 2015.

Formula

a(n) = 2 * A014552(n).

Example

a(1)=0; a(2)=0; a(3)=a(4)=2 since {{2,3,1,2,1,3},{3,1,2,1,3,2}} and {{4,1,3,1,2,4,3,2},{2,3,4,2,1,3,1,4}} are the only ways to permute {1,2,3,1,2,3} and {1,2,3,4,1,2,3,4}, respectively, such that there is one number between the 1's, two numbers between the 2's,..., n numbers between the n's.

Prog

(Sage) a=lambda n:sum(1 for i in DLXCPP([(i-1, j+n, i+j+n+1)for i in[1..n]for j in[0..n+n-i-2]]+[(i, )for i in[n..n+n-1]]))if n%4 in[0, 3] else 0
# Tomas Boothby, Jun 14 2013

Crossrefs

Cf. A014552, A059106, A004075, A264813, A268536.

Sequence in context: A281988 A190389 A285485 * A087637 A052458 A004586

Adjacent sequences: A176124 A176125 A176126 * A176128 A176129 A176130

Keyword

nonn,hard,more,nice

Author

Andrew McFarland, Apr 09 2010

Extensions

Edited and more terms added from A014552 by Max Alekseyev, May 31 2011, May 19 2015

Corrected and extended using results from the Assarpour et al. (2015) paper by N. J. A. Sloane, Feb 22 2016 at the suggestion of William Rex Marshall.

Status

approved