%I #4 Jan 07 2018 11:02:11
%S 0,0,0,0,1,0,0,2,2,0,0,5,4,5,0,0,10,13,13,10,0,0,25,62,15,62,25,0,0,
%T 54,222,233,233,222,54,0,0,125,820,1052,2621,1052,820,125,0,0,282,
%U 3159,5774,21519,21519,5774,3159,282,0,0,641,11882,36119,174970,284344,174970
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0...0.....0......0........0.........0...........0.............0..............0
%C .0...1.....2......5.......10........25..........54...........125............282
%C .0...2.....4.....13.......62.......222.........820..........3159..........11882
%C .0...5....13.....15......233......1052........5774.........36119.........204522
%C .0..10....62....233.....2621.....21519......174970.......1556367.......13214094
%C .0..25...222...1052....21519....284344.....3740362......52727368......711614693
%C .0..54...820...5774...174970...3740362....76517448....1699781649....36000744495
%C .0.125..3159..36119..1556367..52727368..1699781649...58344517697..1923723833047
%C .0.282.11882.204522.13214094.711614693.36000744495.1923723833047.99045666327382
%H R. H. Hardin, <a href="/A297866/b297866.txt">Table of n, a(n) for n = 1..197</a>
%F Empirical for column k:
%F k=1: a(n) =
%F k=2: a(n) = 3*a(n-2) +4*a(n-3) +2*a(n-4)
%F k=3: [order 14] for n>16
%F k=4: [order 47] for n>50
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..1
%e ..0..1..0..1. .0..1..1..0. .1..0..1..1. .1..0..0..1. .0..1..0..1
%e ..0..1..1..1. .1..1..0..1. .1..1..0..0. .1..1..1..1. .0..0..1..0
%e ..1..0..0..0. .1..0..0..1. .1..0..0..1. .0..1..0..0. .0..1..1..0
%e ..1..1..0..0. .1..1..1..1. .0..0..1..1. .0..0..0..0. .1..1..0..0
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 07 2018