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%I #4 Feb 06 2018 13:38:54
%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,29,29,23,5,8,49,63,112,63,49,8,
%T 13,99,199,504,504,199,99,13,21,189,593,2528,3463,2528,593,189,21,34,
%U 383,1657,11252,24519,24519,11252,1657,383,34,55,777,4689,50720,167810
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0...1....1......2.......3.........5...........8...........13.............21
%C ..1...3....7.....13......23........49..........99..........189............383
%C ..1...7...15.....29......63.......199.........593.........1657...........4689
%C ..2..13...29....112.....504......2528.......11252........50720.........241309
%C ..3..23...63....504....3463.....24519......167810......1165033........8305148
%C ..5..49..199...2528...24519....270346.....3203795.....36378590......417642077
%C ..8..99..593..11252..167810...3203795....60731972...1089584523....20249517439
%C .13.189.1657..50720.1165033..36378590..1089584523..30975700202...924197633148
%C .21.383.4689.241309.8305148.417642077.20249517439.924197633148.44405195921475
%H R. H. Hardin, <a href="/A299314/b299314.txt">Table of n, a(n) for n = 1..180</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 16] for n>17
%F k=4: [order 62] for n>66
%e Some solutions for n=5 k=4
%e ..0..1..0..0. .0..0..1..0. .0..1..1..0. .0..0..0..0. .0..1..1..0
%e ..0..1..1..1. .1..1..1..0. .0..0..0..1. .1..0..0..1. .0..0..1..0
%e ..0..1..1..0. .0..0..1..1. .0..0..0..1. .0..1..0..1. .0..0..1..1
%e ..0..1..1..0. .1..0..1..1. .1..0..0..1. .1..0..0..1. .0..0..1..1
%e ..0..1..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297953.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 06 2018
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