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T(n,k)=Number of nXk arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without move-in move-out left turns
5

%I #4 Jan 25 2013 05:24:58

%S 1,3,3,8,27,8,21,240,240,21,55,2127,7371,2127,55,144,18828,225873,

%T 225873,18828,144,377,166581,6916881,23965217,6916881,166581,377,987,

%U 1473549,211747695,2541024755,2541024755,211747695,1473549,987,2584,13033908

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

%C Table starts

%C ....1.........3............8.............21..............55.............144

%C ....3........27..........240...........2127...........18828..........166581

%C ....8.......240.........7371.........225873.........6916881.......211747695

%C ...21......2127.......225873.......23965217......2541024755....269350655878

%C ...55.....18828......6916881.....2541024755....932759231192.342291992210642

%C ..144....166581....211747695...269350655878.342291992210642

%C ..377...1473549...6481445220.28548644230368

%C ..987..13033908.198382906386

%C .2584.115285587

%C .6765

%H R. H. Hardin, <a href="/A221773/b221773.txt">Table of n, a(n) for n = 1..60</a>

%e Some solutions for n=3 k=4

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

%e ..1..2..4..0....3..0..3..2....1..3..2..1....1..2..2..3....1..0..1..2

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

%Y Column 1 is A001906

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_ Jan 25 2013