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%I #8 Nov 21 2014 03:55:50
%S 81,260,260,702,636,702,1786,1220,1220,1786,4621,2356,1310,2356,4621,
%T 11936,4500,1488,1488,4500,11936,30656,8594,2086,2012,2086,8594,30656,
%U 77576,16448,2900,2816,2816,2900,16448,77576,200452,31672,4132,4440,4622
%N T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with the upper median of every 2 X 2 subblock differing from its horizontal and vertical neighbors by exactly one.
%C Table starts:
%C .....81....260...702..1786..4621.11936.30656.77576.200452.515424.1325424
%C ....260....636..1220..2356..4500..8594.16448.31672..60362.116180..223768
%C ....702...1220..1310..1488..2086..2900..4132..5720...8248..11504...16546
%C ...1786...2356..1488..2012..2816..4440..5976.10104..14168..22294...29908
%C ...4621...4500..2086..2816..4622..5656..7756.11312..17626..22624...30496
%C ..11936...8594..2900..4440..5656..9368.11984.20756..28336..47134...59920
%C ..30656..16448..4132..5976..7756.11984.18344.23968..35732..47936...71426
%C ..77576..31672..5720.10104.11312.20756.23968.44292..56672..98684..119840
%C .200452..60362..8248.14168.17626.28336.35732.56672.102536.113344..166116
%C .515424.116180.11504.22294.22624.47134.47936.98684.113344.211268..239680
%H R. H. Hardin, <a href="/A237637/b237637.txt">Table of n, a(n) for n = 1..2664</a>
%F Empirical for column k:
%F k=1: a(n) = 36*a(n-4) +48*a(n-6) for n>9.
%F k=2: a(n) = 3*a(n-3) +10*a(n-4) -12*a(n-7) -6*a(n-8) for n>12.
%F k=3: a(n) = 4*a(n-4) for n>13.
%F k=4: a(n) = 5*a(n-4) for n>14.
%F k=5: a(n) = 4*a(n-4) for n>13.
%F k=6: a(n) = 5*a(n-4) for n>14.
%F k=7: a(n) = 4*a(n-4) for n>15.
%F diagonal: a(n) = 4*a(n-2) +25*a(n-4) -100*a(n-6) for n>11.
%e Some solutions for n=5, k=4:
%e ..1..1..0..1..2....0..0..0..1..2....2..1..0..2..1....2..1..0..1..2
%e ..0..0..0..2..1....2..1..0..1..2....0..2..0..0..0....0..0..0..2..1
%e ..0..1..2..1..0....1..2..0..0..0....0..1..2..1..0....0..1..2..1..0
%e ..1..2..0..0..0....0..0..2..1..0....0..0..0..2..1....0..2..0..0..0
%e ..2..1..0..1..2....1..0..1..2..0....1..2..0..1..2....2..1..0..1..2
%e ..1..0..0..2..1....1..0..0..1..2....2..1..0..0..1....1..0..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 10 2014
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