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%I #4 Jan 25 2013 07:49:55
%S 1,3,3,8,35,8,21,372,372,21,55,3943,16384,3943,55,144,41745,703148,
%T 703148,41745,144,377,441877,30088757,120493257,30088757,441877,377,
%U 987,4677106,1287149604,20501683580,20501683580,1287149604,4677106,987,2584
%N T(n,k)=Number of nXk arrays of occupancy after each element stays put or moves to some king-move neighbor, without move-in move-out left turns
%C Table starts
%C ...1.......3..........8..........21..........55...........144.........377
%C ...3......35........372........3943.......41745........441877.....4677106
%C ...8.....372......16384......703148....30088757....1287149604.55062005315
%C ..21....3943.....703148...120493257.20501683580.3483716568676
%C ..55...41745...30088757.20501683580
%C .144..441877.1287149604
%C .377.4677106
%C .987
%H R. H. Hardin, <a href="/A221776/b221776.txt">Table of n, a(n) for n = 1..40</a>
%e Some solutions for n=3 k=4
%e ..0..0..1..1....0..3..0..1....0..0..0..1....0..1..1..3....0..1..0..2
%e ..0..3..1..0....0..3..1..4....0..3..2..1....0..0..0..0....0..2..0..3
%e ..2..3..0..1....0..0..0..0....2..2..0..1....0..6..1..0....1..1..2..0
%Y Column 1 is A001906
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Jan 25 2013