%I A001171 M3570 N1447
%S A001171 1,1,4,20,148,1348,15104,198144,2998656,51290496
%N A001171 From least significant term in expansion of E( tr (X'*X)^n ), X rectangular 
               and Gaussian. Also number of types of sequential n-swap moves for 
               traveling salesman problem.
%C A001171 Let X be a p X q rectangular matrix with random Gaussian entries. Expand 
               E( tr (X'*X)^n ) as a polynomial in p and q for fixed n. Sequence 
               gives coefficient of least significant term in polynomial.
%C A001171 There should be a reference to a paper by Guy et al. (?) that gives a 
               formula.
%C A001171 An n-swap move consists of the removal of n edges and addition of n different 
               edges which result in a new tour. A sequential n-swap is one in which 
               the union of the n removed and n added edges forms a single cycle. 
               The type can be characterized by how the n segments of the original 
               tour formed by the removal are reassembled.
%D A001171 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001171 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001171 P. J. Hanlon, R. P. Stanley and J. R. Stembridge, Some combinatorial 
               aspects of the spectra of normally distributed random matrices. Hypergeometric 
               functions on domains of positivity, Jack polynomials and applications 
               (Tampa, FL, 1991), 151-174, Contemp. Math., 138, Amer. Math. Soc., 
               Providence, RI, 1992.
%D A001171 David L. Applegate, Robert E. Bixby, Vasek Chvatal and William J. Cook, 
               The Traveling Salesman Problem: A Computational Study, Princeton 
               UP, 2006, Table 17.1, p. 535 (has 1358 instead of 1348 for n = 6)
%H A001171 Keld Helsgaun, <a href="http://www.akira.ruc.dk/~keld/research/LKH/KoptReport.pdf">
               An Effective Implementation of K-opt Movesfor the Lin-Kernighan TSP 
               Heuristic</a>.
%F A001171 Hanlon et al. give a formula (it would be nice to give it here).
%F A001171 A complicated formula from Hanlon is given on page 23 of Helsgaun. - 
               Rob Pratt (Rob.Pratt(AT)sas.com), Mar 30 2007
%Y A001171 Cf. A061714.
%Y A001171 Sequence in context: A144009 A117887 A082988 this_sequence A167018 A094070 
               A119022
%Y A001171 Adjacent sequences: A001168 A001169 A001170 this_sequence A001172 A001173 
               A001174
%K A001171 nonn,nice
%O A001171 1,3
%A A001171 C. L. Mallows (colinm(AT)research.avayalabs.com)
%E A001171 Additional comments from David Applegate (david(AT)research.att.com), 
               Jun 21 2001