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T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns
13

%I #4 Jan 20 2013 19:58:13

%S 0,1,0,2,2,0,4,10,4,0,8,53,54,8,0,16,269,811,287,16,0,32,1378,11344,

%T 12270,1522,32,0,64,7057,160999,472974,184193,8072,64,0,128,36152,

%U 2286878,18561474,19521328,2764070,42810,128,0,256,185192,32522604

%N T(n,k)=Number of nXk arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns

%C Table starts

%C .0....1........2............4..............8...............16................32

%C .0....2.......10...........53............269.............1378..............7057

%C .0....4.......54..........811..........11344...........160999...........2286878

%C .0....8......287........12270.........472974.........18561474.........730077217

%C .0...16.....1522.......184193.......19521328.......2114436826......229719706276

%C .0...32.....8072......2764070......804371949.....240257613761....72063803799931

%C .0...64....42810.....41480899....33145684280...27294219603383.22596355738886108

%C .0..128...227042....622510123..1365843685939.3100806305382481

%C .0..256..1204112...9342086217.56282519118170

%C .0..512..6385980.140197824897

%C .0.1024.33867896

%C .0.2048

%H R. H. Hardin, <a href="/A221609/b221609.txt">Table of n, a(n) for n = 1..95</a>

%e Some solutions for n=3 k=4

%e ..1..1..1..1....0..2..2..1....1..2..1..0....0..3..1..1....0..2..1..1

%e ..0..3..1..0....0..1..1..0....0..2..1..1....0..1..2..0....0..1..1..1

%e ..1..1..2..0....1..2..2..0....1..1..2..0....1..1..2..0....2..1..2..0

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Jan 20 2013