%I #4 Jan 13 2017 07:22:26
%S 0,0,0,0,0,0,0,2,2,0,0,12,96,12,0,0,58,532,532,58,0,0,252,2321,2324,
%T 2321,252,0,0,1048,8886,9854,9854,8886,1048,0,0,4204,31700,38972,
%U 44395,38972,31700,4204,0,0,16454,108034,146606,184290,184290,146606,108034,16454,0
%N T(n,k)=Number of nXk 0..1 arrays with no element equal to more than three of its kingmove neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C .0.....0.......0.......0........0.........0.........0..........0..........0
%C .0.....0.......2......12.......58.......252......1048.......4204......16454
%C .0.....2......96.....532.....2321......8886.....31700.....108034.....357542
%C .0....12.....532....2324.....9854.....38972....146606.....533340....1896352
%C .0....58....2321....9854....44395....184290....722952....2696692....9734320
%C .0...252....8886...38972...184290....770788...3042556...11471132...41949794
%C .0..1048...31700..146606...722952...3042556..12164474...46511454..172759149
%C .0..4204..108034..533340..2696692..11471132..46511454..180119924..677915790
%C .0.16454..357542.1896352..9734320..41949794.172759149..677915790.2586759715
%C .0.63236.1158596.6625144.34378916.150344672.628675456.2501817200.9677601094
%H R. H. Hardin, <a href="/A281034/b281034.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n1)
%F k=2: [order 10]
%F k=3: [order 18] for n>21
%F k=4: [order 36] for n>41
%F k=5: [order 98] for n>109
%e Some solutions for n=4 k=4
%e ..0..1..0..1. .0..0..0..0. .0..0..0..1. .0..1..1..0. .0..0..1..1
%e ..0..1..0..1. .1..1..1..1. .0..1..0..0. .1..1..0..1. .1..0..0..1
%e ..0..0..0..1. .0..1..0..0. .0..1..1..1. .0..0..0..1. .1..1..1..0
%e ..0..1..0..1. .0..1..0..0. .1..0..0..0. .0..1..1..0. .1..0..0..0
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 13 2017
