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%I #6 Feb 02 2018 10:27:07
%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 13,99,113,237,237,113,99,13,21,189,261,844,765,844,261,189,21,34,383,
%U 601,2551,3284,3284,2551,601,383,34,55,777,1397,7941,14482,16521,14482,7941
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 7 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.....113......261.......601.......1397........3223
%C ..2..13...25....78....237.....844.....2551......7941......25802.......82080
%C ..3..23...47...237....765....3284....14482.....53272.....215514......912084
%C ..5..49..113...844...3284...16521....90381....457878....2383346....12834179
%C ..8..99..261..2551..14482...90381...708805...4703257...33115108...242951715
%C .13.189..601..7941..53272..457878..4703257..40964223..383092595..3711048926
%C .21.383.1397.25802.215514.2383346.33115108.383092595.4776371282.61947087103
%H R. H. Hardin, <a href="/A298582/b298582.txt">Table of n, a(n) for n = 1..199</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 14] for n>15
%F k=4: [order 68] for n>69
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0
%e ..0..0..1..1. .1..1..0..0. .0..0..1..0. .0..1..0..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .1..0..0..0
%e ..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297953.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jan 22 2018
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