%I #4 Aug 07 2018 22:08:49

%S 0,1,1,1,5,1,2,16,16,2,3,50,35,50,3,5,160,135,135,160,5,8,511,356,702,

%T 356,511,8,13,1634,1113,2726,2726,1113,1634,13,21,5226,3150,11768,

%U 8556,11768,3150,5226,21,34,16716,9484,48526,47374,47374,48526,9484,16716,34

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1.....1......2.......3........5.........8.........13..........21

%C ..1.....5....16.....50.....160......511......1634.......5226.......16716

%C ..1....16....35....135.....356.....1113......3150.......9484.......27522

%C ..2....50...135....702....2726....11768.....48526.....203049......846901

%C ..3...160...356...2726....8556....47374....179111.....878802.....3604079

%C ..5...511..1113..11768...47374...296968...1458418....8231398....43470698

%C ..8..1634..3150..48526..179111..1458418...7370716...49813114...285365386

%C .13..5226..9484.203049..878802..8231398..49813114..384248160..2679172247

%C .21.16716.27522.846901.3604079.43470698.285365386.2679172247.21424520640

%H R. H. Hardin, <a href="/A317823/b317823.txt">Table of n, a(n) for n = 1..363</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)

%F k=3: [order 16] for n>18

%F k=4: [order 37] for n>43

%F k=5: [order 94] for n>99

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 07 2018