%I #4 Jun 10 2018 09:43:24

%S 1,2,2,4,8,4,8,23,23,8,16,65,81,65,16,32,192,292,292,192,32,64,569,

%T 1096,1481,1096,569,64,128,1709,4172,7528,7528,4172,1709,128,256,5162,

%U 15953,38623,51586,38623,15953,5162,256,512,15663,61111,199257,362200,362200

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 5 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.....23......65.......192........569........1709..........5162

%C ...4....23.....81.....292......1096.......4172.......15953.........61111

%C ...8....65....292....1481......7528......38623......199257.......1028731

%C ..16...192...1096....7528.....51586.....362200.....2553685......18030904

%C ..32...569...4172...38623....362200....3492739....33891076.....329477646

%C ..64..1709..15953..199257...2553685...33891076...453853629....6095547869

%C .128..5162..61111.1028731..18030904..329477646..6095547869..113299205109

%C .256.15663.234288.5312551.127390570.3206311981.81987206051.2110390711467

%H R. H. Hardin, <a href="/A305776/b305776.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) = 3*a(n-1) +3*a(n-2) -6*a(n-3) -8*a(n-4) for n>5

%F k=3: [order 16]

%F k=4: [order 57] for n>59

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A304304.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 10 2018