%I #4 Dec 19 2017 13:18:08
%S 2,3,3,5,9,5,8,21,21,8,13,57,69,57,13,21,153,258,258,153,21,34,393,
%T 963,1463,963,393,34,55,1041,3493,8315,8315,3493,1041,55,89,2745,
%U 12860,44668,72533,44668,12860,2745,89,144,7185,47305,246923,579857,579857,246923
%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.
%C Table starts
%C ..2....3......5.......8........13..........21...........34.............55
%C ..3....9.....21......57.......153.........393.........1041...........2745
%C ..5...21.....69.....258.......963........3493........12860..........47305
%C ..8...57....258....1463......8315.......44668.......246923........1364492
%C .13..153....963....8315.....72533......579857......4846823.......40521141
%C .21..393...3493...44668....579857.....6829945.....84312938.....1042553987
%C .34.1041..12860..246923...4846823....84312938...1554755519....28740762011
%C .55.2745..47305.1364492..40521141..1042553987..28740762011...795154816254
%C .89.7185.173498.7488185.334815607.12735280455.523224064059.21598350633016
%H R. H. Hardin, <a href="/A296725/b296725.txt">Table of n, a(n) for n = 1..238</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = a(n-1) +2*a(n-2) +6*a(n-3)
%F k=3: [order 10]
%F k=4: [order 18]
%F k=5: [order 45]
%e Some solutions for n=5 k=4
%e ..1..0..0..0. .1..0..0..1. .0..0..0..0. .1..0..1..1. .0..0..0..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..1..0. .0..0..0..0
%e ..0..0..1..0. .0..0..1..0. .1..1..0..0. .1..0..0..0. .0..0..0..0
%e ..0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..0..1. .0..1..0..0
%e ..1..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
%Y Column 1 is A000045(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 19 2017