%I #4 Nov 23 2013 06:42:16
%S 1,3,3,7,23,7,15,145,145,15,33,887,2411,887,33,73,5487,39321,39321,
%T 5487,73,161,33957,647287,1704619,647287,33957,161,355,210039,
%U 10652849,74665511,74665511,10652849,210039,355,783,1299219,175284259,3271362341
%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 or vertically
%C Table starts
%C ...1.......3..........7............15................33...................73
%C ...3......23........145...........887..............5487................33957
%C ...7.....145.......2411.........39321............647287.............10652849
%C ..15.....887......39321.......1704619..........74665511...........3271362341
%C ..33....5487.....647287......74665511........8716796353........1017627171097
%C ..73...33957...10652849....3271362341.....1017627171097......316516682114845
%C .161..210039..175284259..143280358783...118759183620445....98411994699167317
%C .355.1299219.2884208601.6275473692531.13859593192739275.30598926533212575781
%H R. H. Hardin, <a href="/A232368/b232368.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +a(n-3)
%F k=2: a(n) = 5*a(n-1) +6*a(n-2) +8*a(n-3) +3*a(n-4) -8*a(n-5) -5*a(n-6)
%F k=3: [order 21]
%F k=4: [order 60]
%e Some solutions for n=3 k=4
%e ..0..1..2..2....1..0..2..1....2..2..1..0....1..2..1..1....2..1..2..1
%e ..2..1..1..2....2..1..0..1....0..1..1..1....0..1..2..2....1..1..2..2
%e ..1..2..2..1....2..1..1..2....2..2..2..2....2..2..2..1....2..0..2..2
%Y Column 1 is A193641
%Y Column 2 is A232145
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 23 2013