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%I M3452 N1403 #38 Sep 03 2023 20:59:15
%S 1,4,12,36,108,324,948,2796,8196,24060,70188,205284,597996,1744548,
%T 5073900,14774652,42922452,124814484,362267652,1052271732,3051900516,
%U 8857050204,25671988020,74449697484,215677847460,625096195404,1810062340812,5243388472212
%N Number of n-step self-avoiding walks on diamond.
%C Number of 2 X n binary matrices avoiding simultaneously the right-angled numbered polyomino patterns (ranpp) (00;1) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1 < i2, j1 < j2 and these elements are in same relative order as those in the triple (x,y,z). - _Sergey Kitaev_, Nov 11 2004
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. W. Essam and M. F. Sykes, <a href="http://dx.doi.org/10.1016/S0031-8914(63)80297-9">The crystal statistics of the diamond lattice</a>, Physica, 29 (1963), 378-388.
%H A. J. Guttmann, <a href="http://dx.doi.org/10.1088/0305-4470/22/14/027">On the critical behavior of self-avoiding walks II</a>, J. Phys. A 22 (1989), 2807-2813.
%H S. Kitaev, <a href="http://www.emis.de/journals/INTEGERS/papers/e21/e21.Abstract.html">On multi-avoidance of right angled numbered polyomino patterns</a>, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
%H S. Kitaev, <a href="https://web.archive.org/web/20130625171839/http://www.ms.uky.edu/~math/MAreport/4-ser.ps">On multi-avoidance of right angled numbered polyomino patterns</a>, University of Kentucky Research Reports (2004).
%H J. L. Martin, <a href="http://dx.doi.org/10.1017/S0305004100036240">The exact enumeration of self-avoiding walks on a lattice</a>, Proc. Camb. Phil. Soc., 58 (1962), 92-101.
%Y Cf. A001395, A001396, A001397, A001398, A097700, A176086, A227715, A227716.
%K nonn,walk,nice
%O 0,2
%A _N. J. A. Sloane_
%E Edited and extended by _Joseph Myers_, Jul 21 2013
%E a(24)-a(27) from _Sean A. Irvine_, Nov 13 2017
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