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%I #4 Dec 20 2014 13:40:33
%S 46,96,96,148,142,148,394,204,204,394,707,519,134,519,707,1982,1047,
%T 407,407,1047,1982,3703,2719,291,1480,291,2719,3703,10772,6483,881,
%U 2048,2048,881,6483,10772,20437,16887,727,6246,568,6246,727,16887,20437,60042
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every consecutive three elements in every row and column having exactly two distinct values, and in every diagonal and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order
%C Table starts
%C ....46.....96..148....394...707...1982...3703...10772..20437...60042..115343
%C ....96....142..204....519..1047...2719...6483...16887..42825..111655..288975
%C ...148....204..134....407...291....881....727....2067...2067....5331....6491
%C ...394....519..407...1480..2048...6246..12740...35128..84680..225000..573968
%C ...707...1047..291...2048...568...4138...1276....8608...3244...18576....9144
%C ..1982...2719..881...6246..4138..18940..25382...82842.168598..474106.1144322
%C ..3703...6483..727..12740..1276..25382...2592...51060...5944..103716...15052
%C .10772..16887.2067..35128..8608..82842..51060..255112.337036.1125816.2286048
%C .20437..42825.2067..84680..3244.168598...5944..337036..12400..675756...28596
%C .60042.111655.5331.225000.18576.474106.103716.1125816.675756.3480808.4572432
%H R. H. Hardin, <a href="/A252695/b252695.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 13] for n>14
%F k=2: [order 10] for n>11
%F k=3: [order 9] for n>10
%F k=4: [order 10] for n>11
%F k=5: [order 9] for n>10
%F k=6: [order 10] for n>11
%F k=7: [order 9] for n>10
%e Some solutions for n=4 k=4
%e ..0..1..0..1..0..1....0..1..0..1..0..1....0..1..1..2..2..1....0..1..1..0..0..1
%e ..2..3..2..3..2..3....2..3..2..3..2..3....2..3..3..0..0..3....2..3..3..2..2..3
%e ..2..3..2..3..2..3....2..3..2..3..2..3....2..1..1..2..2..3....2..1..1..0..0..1
%e ..0..1..0..1..0..1....0..1..0..1..0..1....0..3..3..0..0..1....0..3..3..2..2..1
%e ..0..1..0..1..0..1....0..1..0..1..0..1....2..1..1..2..2..1....2..1..1..0..0..3
%e ..2..2..3..2..3..2....3..3..2..2..3..2....2..3..3..0..0..3....2..3..3..2..2..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 20 2014
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