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%I #4 Jan 13 2018 11:39:50
%S 1,2,2,3,4,3,5,4,4,5,8,16,6,16,8,13,50,18,18,50,13,21,112,15,196,15,
%T 112,21,34,348,104,497,497,104,348,34,55,1028,227,2618,1822,2618,227,
%U 1028,55,89,2796,510,15694,7250,7250,15694,510,2796,89,144,8216,2020,74848,72678
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1....2....3......5.......8........13.........21...........34.............55
%C ..2....4....4.....16......50.......112........348.........1028...........2796
%C ..3....4....6.....18......15.......104........227..........510...........2020
%C ..5...16...18....196.....497......2618......15694........74848.........398520
%C ..8...50...15....497....1822......7250......72678.......448220........2829887
%C .13..112..104...2618....7250....111350....1177545.....10544116......137536697
%C .21..348..227..15694...72678...1177545...25625864....356815204.....6737133411
%C .34.1028..510..74848..448220..10544116..356815204...7382868491...216982050084
%C .55.2796.2020.398520.2829887.137536697.6737133411.216982050084.11381281119654
%H R. H. Hardin, <a href="/A298154/b298154.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) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6
%F k=3: [order 18] for n>19
%F k=4: [order 66] for n>68
%e Some solutions for n=6 k=4
%e ..0..1..1..0. .0..0..1..0. .0..1..1..0. .0..1..0..1. .0..1..1..1
%e ..1..1..0..1. .0..0..1..0. .1..0..1..1. .1..0..0..0. .1..1..0..0
%e ..0..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..0. .1..1..0..0
%e ..1..1..0..1. .0..0..1..0. .0..0..0..1. .1..1..0..1. .1..1..0..1
%e ..0..1..0..0. .1..1..1..1. .1..1..0..0. .1..0..0..0. .0..1..0..0
%e ..0..1..0..0. .0..0..1..1. .1..1..0..0. .0..1..0..1. .1..0..0..0
%Y Column 1 is A000045(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 13 2018
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