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%I #4 Dec 25 2014 13:51:09
%S 202,829,829,3548,4315,3548,15395,24001,24001,15395,66914,136697,
%T 176608,136697,66914,291448,782043,1350439,1350439,782043,291448,
%U 1269628,4486592,10388030,14090659,10388030,4486592,1269628,5531792,25761550
%N T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every consecutive three elements in every row and column having exactly 2 distinct values, in every diagonal 1 or 2 distinct values, in every antidiagonal 2 or 3 distinct values, and new values 0 upwards introduced in row major order
%C Table starts
%C ......202.......829........3548.........15395..........66914..........291448
%C ......829......4315.......24001........136697.........782043.........4486592
%C .....3548.....24001......176608.......1350439.......10388030........80232248
%C ....15395....136697.....1350439......14090659......147972602......1564485159
%C ....66914....782043....10388030.....147972602.....2130083253.....30940948009
%C ...291448...4486592....80232248....1564485159....30940948009....618832488265
%C ..1269628..25761550...620852707...16592413774...451039578594..12432368877884
%C ..5531792.147992920..4808767844..176117806795..6583353528238.250255753857694
%C .24108466.850428880.37257749515.1870443952223.96167118477959
%H R. H. Hardin, <a href="/A252993/b252993.txt">Table of n, a(n) for n = 1..92</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 52]
%e Some solutions for n=3 k=4
%e ..0..0..1..1..2..1....0..0..1..0..0..1....0..0..1..0..0..1....0..0..1..1..0..1
%e ..0..2..2..0..2..2....1..0..1..1..0..1....0..0..1..1..0..0....0..2..2..1..2..2
%e ..2..0..2..0..0..1....0..2..2..1..1..2....1..1..0..0..2..0....2..0..2..2..0..2
%e ..2..2..1..1..2..1....0..0..2..2..0..2....0..1..1..0..0..1....2..2..1..1..0..0
%e ..0..0..2..0..2..0....1..2..1..1..0..1....1..0..1..1..0..0....1..2..2..1..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 25 2014