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Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,0,2,2 for x=0,1,2,3,4
1

%I #5 Mar 31 2012 12:36:29

%S 3,23,84,583,2233,10758,53337,252125,1209824,5768661,27595593,

%T 132068806,631286751,3018734589,14435100274,69026970467,330080196953,

%U 1578377336418,7547555375561,36091265919103,172582773358524,825263869695369

%N Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,3,0,2,2 for x=0,1,2,3,4

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

%C Column 4 of A197457

%H R. H. Hardin, <a href="/A197453/b197453.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +6*a(n-2) +15*a(n-3) +50*a(n-4) +153*a(n-5) +182*a(n-6) +379*a(n-7) +965*a(n-8) +359*a(n-9) -1167*a(n-10) -2472*a(n-11) -4778*a(n-12) -5592*a(n-13) -2203*a(n-14) -350*a(n-15) -2414*a(n-16) +488*a(n-17) +7327*a(n-18) +5913*a(n-19) +7477*a(n-20) +9964*a(n-21) +7136*a(n-22) +12438*a(n-23) +7558*a(n-24) -81*a(n-25) -813*a(n-26) +2186*a(n-27) +2986*a(n-28) +284*a(n-29) -1001*a(n-30) +460*a(n-31) -837*a(n-32) -1033*a(n-33) +93*a(n-34) +254*a(n-35) +6*a(n-36) -33*a(n-37) -8*a(n-38)

%e Some solutions containing all values 0 to 4 for n=5

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

%e ..2..2..3..2....0..0..1..0....2..2..4..2....0..0..1..0....0..2..0..0

%e ..0..0..2..0....0..2..3..2....0..0..2..0....0..2..3..2....1..3..2..0

%e ..2..2..4..2....2..4..2..0....0..1..3..2....2..4..2..0....0..2..4..2

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Oct 15 2011