%I #4 Mar 11 2018 08:42:02
%S 1,1,1,1,3,1,1,2,2,1,1,10,5,10,1,1,13,11,11,13,1,1,42,8,28,8,42,1,1,
%T 74,58,80,80,58,74,1,1,188,131,245,398,245,131,188,1,1,387,306,729,
%U 1382,1382,729,306,387,1,1,885,936,2604,6686,9015,6686,2604,936,885,1,1,1937
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .1...1...1....1......1.......1........1.........1...........1............1
%C .1...3...2...10.....13......42.......74.......188.........387..........885
%C .1...2...5...11......8......58......131.......306.........936.........2435
%C .1..10..11...28.....80.....245......729......2604........8579........27943
%C .1..13...8...80....398....1382.....6686.....30218......131674.......611429
%C .1..42..58..245...1382....9015....54361....338173.....2152660.....13818749
%C .1..74.131..729...6686...54361...494771...4174087....37464671....329141039
%C .1.188.306.2604..30218..338173..4174087..49274326...607495472...7403455976
%C .1.387.936.8579.131674.2152660.37464671.607495472.10215309343.174419385580
%H R. H. Hardin, <a href="/A300682/b300682.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 4*a(n-2) +2*a(n-3) +a(n-5) -3*a(n-6) +a(n-7)
%F k=3: [order 23] for n>26
%F k=4: [order 82] for n>84
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..0..1..1. .0..1..0..0. .0..1..1..1. .0..0..0..0
%e ..0..0..1..0. .0..1..0..1. .1..1..0..1. .1..0..1..0. .0..1..0..1
%e ..1..1..0..0. .0..1..1..0. .1..0..1..1. .1..1..0..0. .1..1..0..0
%e ..1..0..1..0. .0..0..1..1. .0..0..1..0. .1..0..1..1. .1..0..1..0
%e ..0..0..0..1. .0..0..1..0. .1..0..0..0. .0..0..1..1. .0..0..0..1
%Y Column 2 is A300374.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 11 2018