%I #4 Dec 11 2016 08:51:50

%S 1,1,1,1,3,1,2,8,8,2,3,22,35,22,3,5,61,157,157,61,5,8,170,695,1101,

%T 695,170,8,13,472,3157,7905,7905,3157,472,13,21,1310,14243,58009,

%U 92803,58009,14243,1310,21,34,3637,64170,421999,1098640,1098640,421999,64170,3637,34

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

%C Table starts

%C ..1.....1.......1.........2...........3.............5...............8

%C ..1.....3.......8........22..........61...........170.............472

%C ..1.....8......35.......157.........695..........3157...........14243

%C ..2....22.....157......1101........7905.........58009..........421999

%C ..3....61.....695......7905.......92803.......1098640........12957948

%C ..5...170....3157.....58009.....1098640......21144799.......404651396

%C ..8...472...14243....421999....12957948.....404651396.....12564378389

%C .13..1310...64170...3067328...152622739....7733370493....389417147928

%C .21..3637..289200..22304530..1798168331..147824883279..12073180118618

%C .34.10099.1303737.162224094.21189754515.2826526873740.374420804035101

%H R. H. Hardin, <a href="/A279384/b279384.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

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

%F k=3: [order 18]

%F k=4: [order 57] for n>58

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000045(n-1).

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 11 2016