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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. 7

%I

%S 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 68,15,26,120,626,1592,1592,626,120,26,46,208,1603,5888,9042,5888,

%U 1603,208,46,80,358,4030,21882,51568,51568,21882,4030,358,80,139,612,9973,79112

%N 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 Table starts

%C ..0...0.....2......2........5..........8..........15............26

%C ..0...4....10.....20.......38.........68.........120...........208

%C ..2..10....29.....86......240........626........1603..........4030

%C ..2..20....86....400.....1592.......5888.......21882.........79112

%C ..5..38...240...1592.....9042......51568......283450.......1526492

%C ..8..68...626...5888....51568.....429716.....3490152......27850092

%C .15.120..1603..21882...283450....3490152....42093113.....498160278

%C .26.208..4030..79112..1526492...27850092...498160278....8746623144

%C .46.358..9973.281754..8110769..218952412..5812405127..151499712450

%C .80.612.24388.991292.42557410.1701805320.67071788240.2595668095672

%H R. H. Hardin, <a href="/A279268/b279268.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5

%F k=2: a(n) = 3*a(n-1) -a(n-2) -3*a(n-3) +a(n-4) +a(n-5)

%F 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 k=4: [order 28] for n>31

%F k=5: [order 58] for n>69

%e Some solutions for n=4 k=4

%e ..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..1..0..0. .0..1..0..1

%e ..1..0..0..1. .1..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..1..0

%e ..0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..0. .1..0..1..0

%e ..0..1..1..0. .1..0..1..0. .1..1..0..0. .0..1..0..1. .0..1..0..1

%Y Column 1 is A006367(n-1).

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Dec 08 2016

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)