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%I #4 Dec 24 2017 18:13:20
%S 2,3,3,5,10,5,8,32,32,8,13,103,205,103,13,21,350,1292,1292,350,21,34,
%T 1201,8810,16059,8810,1201,34,55,4143,60779,214205,214205,60779,4143,
%U 55,89,14353,419569,2883705,5651413,2883705,419569,14353,89,144,49844
%N T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 1 king-move neighboring 1.
%C Table starts
%C ..2.....3........5..........8............13...............21.................34
%C ..3....10.......32........103...........350.............1201...............4143
%C ..5....32......205.......1292..........8810............60779.............419569
%C ..8...103.....1292......16059........214205..........2883705...........38753117
%C .13...350.....8810.....214205.......5651413........150408381.........3987917885
%C .21..1201....60779....2883705.....150408381.......7919440725.......414777995952
%C .34..4143...419569...38753117....3987917885.....414777995952.....42862620370029
%C .55.14353..2901787..521094462..105763678912...21727028378285...4429615438702673
%C .89.49844.20091572.7010388932.2806435386716.1138816744364625.458096301059196673
%H R. H. Hardin, <a href="/A297073/b297073.txt">Table of n, a(n) for n = 1..263</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 4*a(n-1) -a(n-2) -a(n-3) -4*a(n-4) -8*a(n-5)
%F k=3: [order 11]
%F k=4: [order 23]
%F k=5: [order 58]
%e Some solutions for n=4 k=4
%e ..1..0..0..1. .1..1..1..0. .0..0..1..0. .1..1..0..0. .0..0..1..0
%e ..1..1..1..1. .1..1..1..0. .0..1..1..1. .0..1..0..0. .1..0..1..1
%e ..0..0..1..1. .1..1..1..0. .1..1..1..1. .0..1..1..0. .1..1..0..0
%e ..0..0..1..1. .1..0..1..1. .1..1..0..1. .0..1..1..1. .0..1..0..1
%Y Column 1 is A000045(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 24 2017
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