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%I #8 Sep 20 2023 18:48:55
%S 0,1,0,0,3,0,3,9,9,0,3,24,50,31,0,9,62,221,296,108,0,15,134,822,1922,
%T 1650,366,0,31,277,2669,10491,15511,8666,1205,0,57,542,8068,50690,
%U 124030,118857,43543,3873,0,108,1035,23169,226771,887491,1393359,876704,211650
%N T(n,k) is the number of n X k 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%H R. H. Hardin, <a href="/A279977/b279977.txt">Table of n, a(n) for n = 1..198</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 9*a(n-1) -30*a(n-2) +45*a(n-3) -30*a(n-4) +9*a(n-5) -a(n-6)
%F k=3: [order 9] for n>10
%F k=4: [order 24]
%F k=5: [order 38] for n>39
%F k=6: [order 96] for n>97
%F Empirical for row n:
%F n=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)
%F n=2: [order 8] for n>10
%F n=3: [order 24] for n>30
%F n=4: [order 68] for n>78
%e Table starts:
%e .0.....1.......0.........3...........3............9.............15
%e .0.....3.......9........24..........62..........134............277
%e .0.....9......50.......221.........822.........2669...........8068
%e .0....31.....296......1922.......10491........50690.........226771
%e .0...108....1650.....15511......124030.......887491........5870751
%e .0...366....8666....118857.....1393359.....14787217......144819856
%e .0..1205...43543....876704....15071233....237386464.....3444870482
%e .0..3873..211650...6281773...158391708...3703836674....79672440007
%e .0.12207.1002602..43997218..1627160233..56499013470..1801951754910
%e .0.37859.4652327.302544617.16409869901.846166990079.40020022178950
%e ...
%e Some solutions for n=4 and k=4:
%e ..0..1..0..0. .0..1..0..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
%e ..0..0..1..0. .0..1..1..0. .0..1..0..0. .1..0..1..0. .1..0..1..1
%e ..1..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..0..1. .1..0..1..1
%e ..1..0..0..1. .0..0..1..0. .0..0..0..1. .1..0..0..1. .0..1..0..1
%Y Row 1 is A105423(n-2).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 24 2016
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