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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 4,2,2,0,2 for x=0,1,2,3,4
1

%I #5 Mar 31 2012 12:36:30

%S 1,31,342,2910,25273,251972,2579814,24550379,230860577,2228487362,

%T 21701017288,209232791158,2007839656980,19335726884633,

%U 186641182758431,1799468819059552,17330304902080402,166963816148786657

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

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

%C Column 4 of A197648

%H R. H. Hardin, <a href="/A197644/b197644.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) -12*a(n-2) +125*a(n-3) +1188*a(n-4) -4683*a(n-5) -20426*a(n-6) +23085*a(n-7) -285475*a(n-8) +51944*a(n-9) +3410113*a(n-10) -1616159*a(n-11) +11659968*a(n-12) +70876989*a(n-13) -287458376*a(n-14) -79618646*a(n-15) +126600327*a(n-16) -457268027*a(n-17) +2660774827*a(n-18) +5224619238*a(n-19) -15669734700*a(n-20) +6771218194*a(n-21) +6121483112*a(n-22) -31180263251*a(n-23) +26942793264*a(n-24) +54371560903*a(n-25) -86658907897*a(n-26) +1609458131*a(n-27) -30362436308*a(n-28) +232978747793*a(n-29) -197086970029*a(n-30) +182277578647*a(n-31) -415970917520*a(n-32) +156986155987*a(n-33) +262241730636*a(n-34) -176381184554*a(n-35) +51972930089*a(n-36) -130169769163*a(n-37) +190494666208*a(n-38) -113932599654*a(n-39) -5323724963*a(n-40) +20288901787*a(n-41) +5998341425*a(n-42) +104384441*a(n-43) -9690118586*a(n-44) +7508363536*a(n-45) -1072629312*a(n-46) -1636386688*a(n-47) +676478848*a(n-48) +17783808*a(n-49) -33298432*a(n-50) +5111808*a(n-51) -524288*a(n-52)

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

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_ Oct 16 2011