%I #4 Jan 26 2018 08:46:15
%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,25,25,23,5,8,49,47,78,47,49,8,
%T 13,99,109,233,233,109,99,13,21,189,245,779,682,779,245,189,21,34,383,
%U 545,2359,2603,2603,2359,545,383,34,55,777,1253,7024,11657,11320,11657,7024
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0...1....1.....2......3.......5........8........13.........21..........34
%C ..1...3....7....13.....23......49.......99.......189........383.........777
%C ..1...7...15....25.....47.....109......245.......545.......1253........2859
%C ..2..13...25....78....233.....779.....2359......7024......21572.......66763
%C ..3..23...47...233....682....2603....11657.....39908.....149791......617528
%C ..5..49..109...779...2603...11320....61333....284618....1376511.....6959439
%C ..8..99..245..2359..11657...61333...484813...2887678...18497464...127977516
%C .13.189..545..7024..39908..284618..2887678..22160831..186728055..1683257109
%C .21.383.1253.21572.149791.1376511.18497464.186728055.2093453587.24925712914
%H R. H. Hardin, <a href="/A298775/b298775.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 12] for n>13
%F k=4: [order 62] for n>65
%e Some solutions for n=6 k=5
%e ..0..0..0..1..0. .0..1..0..0..0. .0..1..1..1..0. .0..0..0..0..0
%e ..1..0..0..0..1. .1..0..0..0..1. .1..0..0..0..1. .1..0..0..0..1
%e ..0..1..1..1..0. .0..1..1..1..0. .1..0..0..0..1. .0..1..1..1..0
%e ..0..1..1..1..0. .0..1..1..1..0. .1..0..0..0..1. .0..1..1..1..0
%e ..0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0. .0..1..1..1..0
%e ..1..0..0..0..1. .1..0..0..0..1. .1..1..1..0..1. .1..0..0..0..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297953.
%Y Column 3 is A297954.
%Y Column 4 is A297955.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 26 2018