%I #4 Feb 16 2018 07:26:25
%S 1,2,2,4,8,4,8,26,26,8,16,88,94,88,16,32,298,372,372,298,32,64,1012,
%T 1512,2009,1512,1012,64,128,3440,6133,12076,12076,6133,3440,128,256,
%U 11700,24742,69614,131420,69614,24742,11700,256,512,39804,100035,398314
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1.....2......4........8.........16..........32............64.............128
%C ...2.....8.....26.......88........298........1012..........3440...........11700
%C ...4....26.....94......372.......1512........6133.........24742..........100035
%C ...8....88....372.....2009......12076.......69614........398314.........2305246
%C ..16...298...1512....12076.....131420.....1223912......11202963.......109221761
%C ..32..1012...6133....69614....1223912....17105490.....231836591......3441737079
%C ..64..3440..24742...398314...11202963...231836591....4670821739....105367758168
%C .128.11700.100035..2305246..109221761..3441737079..105367758168...3777344294506
%C .256.39804.404608.13349305.1053093991.50285500321.2312626806147.130056973753183
%H R. H. Hardin, <a href="/A299675/b299675.txt">Table of n, a(n) for n = 1..180</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) +2*a(n-3) -6*a(n-4) -4*a(n-5)
%F k=3: [order 18] for n>19
%F k=4: [order 65] for n>66
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..1..1
%e ..0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..0. .1..0..0..0
%e ..1..0..0..1. .1..0..0..1. .1..1..1..0. .0..0..1..1. .0..0..0..0
%e ..1..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0
%e ..0..0..1..1. .0..1..0..1. .0..1..0..0. .1..1..0..1. .0..1..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A298189.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 16 2018