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%I #4 Jan 26 2013 08:47:05
%S 1,3,3,6,31,6,13,252,252,13,28,2113,6711,2113,28,60,17684,190756,
%T 190756,17684,60,129,147920,5374720,18636989,5374720,147920,129,277,
%U 1237439,151592441,1804472268,1804472268,151592441,1237439,277,595,10351593
%N T(n,k)=Number of nXk arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without consecutive moves in the same direction
%C Table starts
%C ....1........3............6.............13..............28..............60
%C ....3.......31..........252...........2113...........17684..........147920
%C ....6......252.........6711.........190756.........5374720.......151592441
%C ...13.....2113.......190756.......18636989......1804472268....174820457922
%C ...28....17684......5374720.....1804472268....597819977898.198296512455330
%C ...60...147920....151592441...174820457922.198296512455330
%C ..129..1237439...4274867564.16936005698353
%C ..277.10351593.120554575328
%C ..595.86594795
%C .1278
%H R. H. Hardin, <a href="/A221824/b221824.txt">Table of n, a(n) for n = 1..59</a>
%e Some solutions for n=3 k=4
%e ..0..0..0..0....0..1..0..2....0..0..1..2....0..2..1..1....0..2..1..0
%e ..2..3..1..3....3..3..1..0....3..2..1..0....0..2..1..0....2..0..4..0
%e ..1..0..1..1....1..0..1..0....0..1..2..0....1..0..4..0....1..1..1..0
%Y Column 1 is A002478
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_ Jan 26 2013