%I A110128
%S A110128 1,1,2,4,16,44,200,1288,9512,78652,744360,7867148,91310696,1154292796,
%T A110128 15784573160,232050062524,3648471927912,61080818510972,1084657970877416,
%U A110128 20361216987032284,402839381030339816,8377409956454452732
%N A110128 Number of permutations p of 12..n satisfying |p(i+2)-p(i)| not equal 
               to 2 for all 0<i<n-1.
%C A110128 When n is even: 1) Number of ways that n persons seated at a rectangular 
               table with n/2 seats along the two opposite sides can be rearranged 
               in such a way that neighbors are no more neighbors after the rearrangement. 
               2) Number of ways to arrange n kings on an n X n board, with 1 in 
               each row and column, which are non-attacking with respect to the 
               main four quadrants.
%D A110128 Roberto Tauraso, The Dinner Table Problem: The Rectangular Case, INTEGERS, 
               vol. 6 (2006), paper A11
%H A110128 Roberto Tauraso, <a href="http://front.math.ucdavis.edu/math.CO/0507293">
               The Dinner Table Problem: The Rectangular Case</a>
%F A110128 A formula is given in the Tauraso reference
%Y A110128 Cf. A089222, A002464.
%Y A110128 Sequence in context: A048222 A062330 A133465 this_sequence A148279 A101061 
               A148280
%Y A110128 Adjacent sequences: A110125 A110126 A110127 this_sequence A110129 A110130 
               A110131
%K A110128 nonn
%O A110128 0,3
%A A110128 R. Tauraso, A. Nicolosi and G. Minenkov (tauraso(AT)mat.uniroma2.it), 
               Jul 13 2005
%E A110128 Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion 
               of Vladeta Jovovic, Jan 01 2008