%I #6 Jan 20 2024 14:10:38
%S 1,2,2,4,7,4,8,13,13,8,16,29,20,29,16,32,73,44,44,73,32,64,157,123,
%T 174,123,157,64,128,353,343,1052,1052,343,353,128,256,869,957,4488,
%U 6908,4488,957,869,256,512,1993,2710,18758,39124,39124,18758,2710,1993,512,1024
%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2....4......8.......16........32..........64..........128
%C ...2....7...13.....29.......73.......157.........353..........869
%C ...4...13...20.....44......123.......343.........957.........2710
%C ...8...29...44....174.....1052......4488.......18758........89713
%C ..16...73..123...1052.....6908.....39124......259556......1718835
%C ..32..157..343...4488....39124....379236.....3848010.....39235328
%C ..64..353..957..18758...259556...3848010....59666756....931277377
%C .128..869.2710..89713..1718835..39235328...931277377..22388413097
%C .256.1993.7749.409166.11081989.404291236.14739630633.545009501463
%H R. H. Hardin, <a href="/A299015/b299015.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) -5*a(n-2) +10*a(n-3) -24*a(n-4) +16*a(n-5) for n>6.
%F k=3: [order 16] for n>17.
%F k=4: [order 66] for n>70.
%e Some solutions for n=5, k=4
%e ..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..0
%e ..0..0..1..0. .1..1..1..1. .0..0..0..1. .0..1..1..0. .1..1..0..1
%e ..0..0..1..1. .0..0..1..1. .0..0..1..0. .1..1..1..1. .0..0..0..1
%e ..1..0..0..0. .1..0..1..1. .1..0..0..1. .0..0..0..0. .1..0..0..0
%e ..1..0..1..1. .0..0..1..0. .0..1..1..0. .1..1..1..1. .1..0..1..1
%Y Column 1 is A000079(n-1).
%Y Column 2 is A298215.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 31 2018