cp's OEIS Frontend

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.

%I A176127 #34 Oct 22 2017 22:53:22
%S A176127 0,0,2,2,0,0,52,300,0,0,35584,216288,0,0,79619280,653443600,0,0,
%T A176127 513629782560,5272675722400,0,0,7598911885030976,93690316113031872,0,
%U A176127 0,223367222197529806464,3214766521218764786304,0,0
%N 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.
%D A176127 For references, see A014552.
%H A176127 Ali Assarpour, Amotz Bar-Noy, Ou Liuo, <a href="http://arxiv.org/abs/1507.00315">Counting the Number of Langford Skolem Pairings</a>, arXiv:1507.00315 [cs.DM], 2015.
%F A176127 a(n) = 2 * A014552(n).
%e A176127 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.
%o A176127 (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
%o A176127 # _Tomas Boothby_, Jun 14 2013
%Y A176127 Cf. A014552, A059106, A004075, A264813, A268536.
%K A176127 nonn,hard,more,nice
%O A176127 1,3
%A A176127 _Andrew McFarland_, Apr 09 2010
%E A176127 Edited and more terms added from A014552 by _Max Alekseyev_, May 31 2011, May 19 2015
%E A176127 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_.