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%I #4 Nov 03 2013 07:16:35
%S 0,0,0,0,2,0,0,14,2,0,0,32,50,10,0,0,100,128,410,22,0,0,428,644,2080,
%T 2430,70,0,0,1616,5100,20050,18688,16198,186,0,0,5784,33696,310804,
%U 344136,209440,103042,538,0,0,21248,211032,4110640,10631552,7293728
%N T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero
%C Table starts
%C .0....0........0..........0.............0................0..................0
%C .0....2.......14.........32...........100..............428...............1616
%C .0....2.......50........128...........644.............5100..............33696
%C .0...10......410.......2080.........20050...........310804............4110640
%C .0...22.....2430......18688........344136.........10631552..........274004640
%C .0...70....16198.....209440.......7293728........448752816........22665736960
%C .0..186...103042....2150784.....142466422......17477913984......1729680196768
%C .0..538...667690...22847008....2871061676.....702369644524....136193662172048
%C .0.1494..4294910..239510016...57167235796...27889180833188..10596817937397952
%C .0.4230.27706854.2523778080.1143545760606.1112507026382520.828295717027921136
%H R. H. Hardin, <a href="/A231049/b231049.txt">Table of n, a(n) for n = 1..179</a>
%F Empirical for column k:
%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3)
%F k=3: a(n) = 3*a(n-1) +19*a(n-2) +19*a(n-3) +12*a(n-4) -8*a(n-5) +8*a(n-6)
%F k=4: a(n) = 8*a(n-1) +33*a(n-2) -68*a(n-3)
%F k=5: [order 36]
%F k=6: [order 93]
%F Empirical for row n:
%F n=2: a(n) = 3*a(n-1) +8*a(n-3) +6*a(n-4) -4*a(n-5) for n>6
%F n=3: [order 10] for n>11
%F n=4: [order 31] for n>32
%e Some solutions for n=4 k=4
%e ..0..3..0..1....0..1..2..3....0..3..0..1....0..1..0..3....0..1..2..1
%e ..0..1..2..1....2..3..0..3....2..1..2..3....2..3..2..1....0..3..0..1
%e ..2..1..0..3....0..3..2..3....2..1..2..1....0..3..2..1....0..1..2..1
%e ..2..3..2..1....2..1..0..1....0..3..0..1....2..1..0..1....2..3..0..3
%Y Column 2 is A230893
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Nov 03 2013