%I #4 Nov 27 2013 16:23:22

%S 36,212,212,1568,3138,1568,11878,63632,63632,11878,87680,1323984,

%T 3684840,1323984,87680,651678,26350948,223396744,223396744,26350948,

%U 651678,4846056,532378308,12890094328,39425246602,12890094328,532378308,4846056

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, vertically, diagonally or antidiagonally

%C Table starts

%C ......36.........212...........1568..............11878.................87680

%C .....212........3138..........63632............1323984..............26350948

%C ....1568.......63632........3684840..........223396744...........12890094328

%C ...11878.....1323984......223396744........39425246602.........6593726545958

%C ...87680....26350948....12890094328......6593726545958......3186295643132436

%C ..651678...532378308...754650484792...1120549772696776...1566033207755153544

%C .4846056.10773984656.44225213151124.190677413113742328.770628641578865476150

%H R. H. Hardin, <a href="/A232677/b232677.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 8]

%F k=2: [order 25]

%F k=3: [order 53]

%e Some solutions for n=2 k=4

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 27 2013