%I #4 Oct 12 2018 12:30:26
%S 1,2,2,4,8,4,8,28,28,8,16,97,142,97,16,32,338,732,732,338,32,64,1178,
%T 3694,5956,3694,1178,64,128,4105,18754,46516,46516,18754,4105,128,256,
%U 14305,94842,368049,561290,368049,94842,14305,256,512,49850,480321
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1.....2.......4.........8..........16...........32.............64
%C ...2.....8......28........97.........338.........1178...........4105
%C ...4....28.....142.......732........3694........18754..........94842
%C ...8....97.....732......5956.......46516.......368049........2908839
%C ..16...338....3694.....46516......561290......6845143.......83509525
%C ..32..1178...18754....368049.....6845143....127789964.....2392115850
%C ..64..4105...94842...2908839....83509525...2392115850....69104597430
%C .128.14305..480321..22987303..1016183713..44629532699..1987324601389
%C .256.49850.2431390.181744907.12380173295.834140753692.57271367516963
%H R. H. Hardin, <a href="/A320402/b320402.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +a(n-3) -a(n-4)
%F k=3: [order 12] for n>14
%F k=4: [order 40] for n>41
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..0
%e ..0..0..0..0. .1..0..0..1. .1..1..0..0. .1..0..0..1. .0..1..1..1
%e ..1..1..0..0. .0..0..1..1. .1..0..0..1. .1..0..1..0. .1..1..0..1
%e ..0..0..0..0. .0..1..1..1. .1..0..0..1. .1..0..0..0. .1..1..0..1
%e ..0..0..0..0. .1..0..0..0. .1..1..0..1. .1..0..0..1. .0..1..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A318010.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Oct 12 2018