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T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,1,4,0 for x=0,1,2,3,4
7

%I #5 Mar 31 2012 12:36:28

%S 1,1,1,2,5,2,3,14,14,3,4,37,66,37,4,6,104,306,306,104,6,9,290,1489,

%T 2573,1489,290,9,13,803,7106,21826,21826,7106,803,13,19,2233,34021,

%U 183864,331406,183864,34021,2233,19,28,6207,162800,1566649,5021137,5021137

%N T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,2,1,4,0 for x=0,1,2,3,4

%C Every 0 is next to 0 3's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 4's, every 4 is next to 4 0's

%C Table starts

%C ..1.....1.......2.........3............4..............6.................9

%C ..1.....5......14........37..........104............290...............803

%C ..2....14......66.......306.........1489...........7106.............34021

%C ..3....37.....306......2573........21826.........183864...........1566649

%C ..4...104....1489.....21826.......331406........5021137..........76504483

%C ..6...290....7106....183864......5021137......135820428........3683084153

%C ..9...803...34021...1566649.....76504483.....3683084153......178698032203

%C .13..2233..162800..13348347...1160102790....99818807528.....8671417152697

%C .19..6207..779173.113287557..17605551567..2707589789345...420572258618870

%C .28.17242.3731019.961919858.267441999728.73439922027377.20392149427584727

%H R. H. Hardin, <a href="/A197167/b197167.txt">Table of n, a(n) for n = 1..180</a>

%e Some solutions for n=6 k=4

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

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

%e ..0..4..0..1....0..4..0..1....1..0..4..0....0..4..0..0....0..2..0..0

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

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

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

%Y Column 1 is A000930

%Y Column 2 is A196976

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Oct 10 2011