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A279268 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%I A279268 #4 Dec 08 2016 21:07:28
%S A279268 0,0,0,2,4,2,2,10,10,2,5,20,29,20,5,8,38,86,86,38,8,15,68,240,400,240,
%T A279268 68,15,26,120,626,1592,1592,626,120,26,46,208,1603,5888,9042,5888,
%U A279268 1603,208,46,80,358,4030,21882,51568,51568,21882,4030,358,80,139,612,9973,79112
%N A279268 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C A279268 Table starts
%C A279268 ..0...0.....2......2........5..........8..........15............26
%C A279268 ..0...4....10.....20.......38.........68.........120...........208
%C A279268 ..2..10....29.....86......240........626........1603..........4030
%C A279268 ..2..20....86....400.....1592.......5888.......21882.........79112
%C A279268 ..5..38...240...1592.....9042......51568......283450.......1526492
%C A279268 ..8..68...626...5888....51568.....429716.....3490152......27850092
%C A279268 .15.120..1603..21882...283450....3490152....42093113.....498160278
%C A279268 .26.208..4030..79112..1526492...27850092...498160278....8746623144
%C A279268 .46.358..9973.281754..8110769..218952412..5812405127..151499712450
%C A279268 .80.612.24388.991292.42557410.1701805320.67071788240.2595668095672
%H A279268 R. H. Hardin, <a href="/A279268/b279268.txt">Table of n, a(n) for n = 1..180</a>
%F A279268 Empirical for column k:
%F A279268 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5
%F A279268 k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)
%F A279268 k=3: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-3) -4*a(n-4) -a(n-6) for n>9
%F A279268 k=4: [order 28] for n>31
%F A279268 k=5: [order 58] for n>69
%e A279268 Some solutions for n=4 k=4
%e A279268 ..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..1..0..0. .0..1..0..1
%e A279268 ..1..0..0..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..1..0
%e A279268 ..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..0. .1..0..1..0
%e A279268 ..0..1..1..0. .1..0..1..0. .1..1..0..0. .0..1..0..1. .0..1..0..1
%Y A279268 Column 1 is A006367(n-1).
%K A279268 nonn,tabl
%O A279268 1,4
%A A279268 _R. H. Hardin_, Dec 08 2016