%I #4 Jan 18 2018 08:10:27
%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 13,99,167,432,432,167,99,13,21,189,473,1915,2231,1915,473,189,21,34,
%U 383,1205,7556,13271,13271,7556,1205,383,34,55,777,3161,29657,81019,117184
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 or 6 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........473........1205..........3161
%C ..2..13...29....112.....432.....1915.......7556.......29657........123601
%C ..3..23...63....432....2231....13271......81019......454822.......2647771
%C ..5..49..167...1915...13271...117184....1142217.....9792821......87882289
%C ..8..99..473...7556...81019..1142217...16510708...212408711....2962142231
%C .13.189.1205..29657..454822..9792821..212408711..4149393799...87858962506
%C .21.383.3161.123601.2647771.87882289.2962142231.87858962506.2858791588717
%H R. H. Hardin, <a href="/A298396/b298396.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>71
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..1..0. .0..1..0..1. .0..0..0..1. .0..0..0..0
%e ..1..0..0..1. .1..1..0..1. .0..0..1..0. .1..1..1..0. .1..0..0..1
%e ..0..1..0..0. .0..0..0..1. .0..0..1..1. .0..1..1..1. .1..1..1..1
%e ..1..0..0..0. .1..0..0..1. .1..0..1..1. .0..1..0..0. .1..1..0..0
%e ..0..1..1..0. .1..0..1..0. .0..1..0..1. .1..0..1..1. .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_, Jan 18 2018