%I #4 Dec 28 2016 07:04:15

%S 0,1,1,0,2,0,3,12,12,3,3,41,60,41,3,9,103,279,279,103,9,15,263,1082,

%T 1633,1082,263,15,31,656,3931,8759,8759,3931,656,31,57,1618,13720,

%U 43094,63336,43094,13720,1618,57,108,3931,46467,202693,421214,421214,202693,46467

%N 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 two elements, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ...0....1......0........3.........3...........9...........15.............31

%C ...1....2.....12.......41.......103.........263..........656...........1618

%C ...0...12.....60......279......1082........3931........13720..........46467

%C ...3...41....279.....1633......8759.......43094.......202693.........919058

%C ...3..103...1082.....8759.....63336......421214......2665301.......16203600

%C ...9..263...3931....43094....421214.....3755997.....31821879......258976696

%C ..15..656..13720...202693...2665301....31821879....359880117.....3910652938

%C ..31.1618..46467...919058..16203600...258976696...3910652938....56789421603

%C ..57.3931.153650..4057457..95738359..2046791216..41205820599...798794739075

%C .108.9459.499289.17554353.553426602.15814457993.424186764568.10974204206787

%H R. H. Hardin, <a href="/A280180/b280180.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

%F k=2: [order 10] for n>14

%F k=3: [order 21] for n>28

%F k=4: [order 45] for n>54

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A105423(n-2).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 28 2016