%I
%S 1,2,2,3,6,3,4,13,13,4,6,34,51,34,6,9,81,205,205,81,9,13,199,812,1407,
%T 812,199,13,19,487,3295,9492,9492,3295,487,19,28,1190,13286,65251,
%U 109286,65251,13286,1190,28,41,2910,53418,445506,1282123,1282123,445506,53418
%N T(n,k) = Number of n X k 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,1,2,4,0 for x=0,1,2,3,4.
%C Every 0 is next to 0 3's, every 1 is next to 1 1's, every 2 is next to 2 2's, every 3 is next to 3 4's, every 4 is next to 4 0's.
%C Table starts:
%C ..1....2......3.........4...........6.............9..............13
%C ..2....6.....13........34..........81...........199.............487
%C ..3...13.....51.......205.........812..........3295...........13286
%C ..4...34....205......1407........9492.........65251..........445506
%C ..6...81....812......9492......109286.......1282123........14895018
%C ..9..199...3295.....65251.....1282123......25822213.......513380599
%C .13..487..13286....445506....14895018.....513380599.....17446576240
%C .19.1190..53418...3041309...173097490...10204673140....592290047724
%C .28.2910.215148..20782756..2014367937..203083535620..20128502440024
%C .41.7115.866828.142011656.23437273689.4041562578683.683993118482402
%H R. H. Hardin, <a href="/A197079/b197079.txt">Table of n, a(n) for n = 1..179</a>
%e Some solutions for n=6 k=4:
%e ..0..0..1..1....2..2..0..0....1..1..0..1....0..0..1..1....0..0..1..0
%e ..0..0..0..0....2..2..1..1....0..0..0..1....0..0..0..0....0..0..1..0
%e ..0..0..0..1....1..1..0..0....0..0..0..0....2..2..2..2....0..0..2..2
%e ..0..4..0..1....0..0..0..0....0..4..0..0....2..1..1..2....1..0..2..2
%e ..0..0..4..0....0..4..0..1....1..0..0..1....2..0..0..2....1..0..1..1
%e ..0..0..0..0....0..0..0..1....1..0..0..1....2..2..2..2....0..0..0..0
%Y Column 1 is A000930(n+1).
%Y Column 2 is A196906.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Oct 09 2011
