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%I #4 Feb 25 2018 06:31:58
%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 13,99,199,515,515,199,99,13,21,189,629,2713,3776,2713,629,189,21,34,
%U 383,1837,12669,28935,28935,12669,1837,383,34,55,777,5397,59569,212470
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 6, 7 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.......199.........629..........1837...........5397
%C ..2..13...29....112......515......2713.......12669.........59569.........295903
%C ..3..23...63....515.....3776.....28935......212470.......1560065.......11874071
%C ..5..49..199...2713....28935....346593.....4293657......52304635......651028308
%C ..8..99..629..12669...212470...4293657....87633085....1730369641....35186245661
%C .13.189.1837..59569..1560065..52304635..1730369641...55075362479..1818989406366
%C .21.383.5397.295903.11874071.651028308.35186245661.1818989406366.98018916520293
%H R. H. Hardin, <a href="/A300115/b300115.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 56] for n>60
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..1..1..0. .0..1..0..0. .0..1..0..0. .0..0..0..0
%e ..1..0..0..1. .0..0..0..1. .0..1..1..1. .0..1..1..1. .1..0..0..1
%e ..1..0..0..1. .0..0..1..0. .1..1..1..0. .1..1..0..1. .1..0..0..1
%e ..0..1..1..0. .1..0..0..1. .1..1..1..0. .0..0..1..1. .1..0..0..0
%e ..1..1..1..1. .1..0..1..0. .1..0..0..1. .0..1..0..0. .1..0..1..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A297953.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Feb 25 2018
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