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%I #6 May 11 2023 12:50:33
%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 13,99,167,439,439,167,99,13,21,189,477,1950,2336,1950,477,189,21,34,
%U 383,1233,7702,13836,13836,7702,1233,383,34,55,777,3265,30277,84449,122197
%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 8 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......167........477........1233..........3265
%C ..2..13...29....112.....439.....1950.......7702.......30277........126429
%C ..3..23...63....439....2336....13836......84449......477162.......2791607
%C ..5..49..167...1950...13836...122197....1190886....10305454......92938855
%C ..8..99..477...7702...84449..1190886...17345466...225351737....3159884395
%C .13.189.1233..30277..477162.10305454..225351737..4446967161...94825218644
%C .21.383.3265.126429.2791607.92938855.3159884395.94825218644.3109567007082
%H R. H. Hardin, <a href="/A299514/b299514.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 15] for n>17
%F k=4: [order 68] for n>70
%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. .0..0..0..1
%e ..0..0..0..1. .0..0..0..1. .1..0..0..0. .1..0..0..0. .1..1..1..1
%e ..0..0..0..1. .0..0..0..1. .1..0..0..0. .1..0..0..0. .0..1..1..1
%e ..0..0..0..1. .0..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..1..1
%e ..0..1..1..0. .0..1..1..1. .0..1..1..0. .1..1..1..0. .1..0..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 11 2018