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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 3,0,4,1,2 for x=0,1,2,3,4
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%I #4 Mar 31 2012 12:36:25

%S 5,17,26,83,168,346,865,2055,4745,10866,24967,57786,134514,312597,

%T 722915,1670991,3869674,8969607,20789120,48159310,111529135,258315343,

%U 598428365,1386426078,3211799633,7440009880,17234511484,39924363651,92487922123

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

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

%C Column 4 of A196146

%F Empirical: a(n) = 5*a(n-1) -9*a(n-2) +9*a(n-3) -8*a(n-4) +12*a(n-5) -20*a(n-6) -a(n-7) +21*a(n-8) +5*a(n-9) -11*a(n-10) -60*a(n-11) +128*a(n-12) +17*a(n-13) -20*a(n-14) -77*a(n-15) +15*a(n-16) -15*a(n-17) -28*a(n-18) -32*a(n-19) -118*a(n-20) +28*a(n-21) -65*a(n-22) -17*a(n-23) -22*a(n-24) +12*a(n-25) -15*a(n-26) +3*a(n-28)

%e Some solutions for n=5

%e .0.1.3.1...0.1.1.0...0.1.3.1...1.0.0.1...0.0.0.1

%e .0.1.1.0...1.1.1.1...0.1.1.0...1.1.1.1...0.0.0.1

%e .1.3.1.0...1.0.0.1...1.3.3.1...0.1.1.0...1.1.1.3

%e .1.3.1.0...1.1.1.1...3.1.1.1...0.1.1.0...1.1.1.1

%e .0.1.3.1...0.1.1.0...1.0.0.0...1.3.1.0...0.0.0.0

%K nonn

%O 1,1

%A _R. H. Hardin_ Sep 28 2011