%I #4 Nov 22 2013 08:37:26
%S 1,3,3,7,37,7,15,257,257,15,33,1915,5149,1915,33,73,14223,107047,
%T 107047,14223,73,161,105411,2245709,6363511,2245709,105411,161,355,
%U 781873,46996227,382995685,382995685,46996227,781873,355,783,5798587,983668985
%N T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally, vertically or antidiagonally
%C Table starts
%C ....1.........3.............7.................15......................33
%C ....3........37...........257...............1915...................14223
%C ....7.......257..........5149.............107047.................2245709
%C ...15......1915........107047............6363511...............382995685
%C ...33.....14223.......2245709..........382995685.............66287652717
%C ...73....105411......46996227........22952606015..........11412010021707
%C ..161....781873.....983668985......1376103637041........1965722343353835
%C ..355...5798587...20589521605.....82507009197797......338617181188008457
%C ..783..43004317..430963205159...4946765617435461....58328939899371775421
%C .1727.318935945.9020580137409.296587635447682217.10047560921392694812519
%H R. H. Hardin, <a href="/A232309/b232309.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +a(n-3)
%F k=2: a(n) = 6*a(n-1) +9*a(n-2) +11*a(n-3) -a(n-4) +16*a(n-5)
%F k=3: [order 15]
%F k=4: [order 33]
%F k=5: [order 91]
%e Some solutions for n=3 k=4
%e ..2..1..1..1....2..1..1..2....1..2..0..1....2..0..2..2....1..2..2..1
%e ..1..2..0..2....1..2..1..1....1..1..2..1....2..1..2..1....0..1..2..1
%e ..0..2..1..1....1..0..2..0....1..2..1..2....0..0..1..0....1..2..0..2
%Y Column 1 is A193641
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 22 2013