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A280161 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A280161 #4 Dec 27 2016 09:23:55
%S A280161 0,0,0,2,4,2,2,8,8,2,5,18,31,18,5,8,40,94,94,40,8,15,92,305,424,305,
%T A280161 92,15,26,208,950,1854,1854,950,208,26,46,470,2901,7628,10677,7628,
%U A280161 2901,470,46,80,1060,8728,30874,58852,58852,30874,8728,1060,80,139,2384,26068
%N A280161 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C A280161 Table starts
%C A280161 ..0....0.....2......2.......5.........8.........15..........26...........46
%C A280161 ..0....4.....8.....18......40........92........208.........470.........1060
%C A280161 ..2....8....31.....94.....305.......950.......2901........8728........26068
%C A280161 ..2...18....94....424....1854......7628......30874......123312.......488256
%C A280161 ..5...40...305...1854...10677.....58852.....318220.....1695030......8941285
%C A280161 ..8...92...950...7628...58852....434790....3138340....22348406....157294986
%C A280161 .15..208..2901..30874..318220...3138340...30089398...285461736...2671391625
%C A280161 .26..470..8728.123312.1695030..22348406..285461736..3612425586..45045404794
%C A280161 .46.1060.26068.488256.8941285.157294986.2671391625.45045404794.748382706193
%H A280161 R. H. Hardin, <a href="/A280161/b280161.txt">Table of n, a(n) for n = 1..199</a>
%F A280161 Empirical for column k:
%F A280161 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
%F A280161 k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6) for n>8
%F A280161 k=3: [order 14] for n>19
%F A280161 k=4: [order 30] for n>36
%F A280161 k=5: [order 70] for n>80
%e A280161 Some solutions for n=4 k=4
%e A280161 ..0..0..1..1. .0..0..0..0. .0..1..1..1. .0..0..1..1. .0..0..0..0
%e A280161 ..0..1..0..1. .0..0..0..1. .0..1..1..0. .0..0..1..1. .1..1..0..1
%e A280161 ..1..1..1..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .1..0..1..1
%e A280161 ..1..1..0..0. .1..1..1..1. .0..1..0..0. .0..1..0..0. .0..0..1..1
%Y A280161 Column 1 is A006367(n-1).
%K A280161 nonn,tabl
%O A280161 1,4
%A A280161 _R. H. Hardin_, Dec 27 2016