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%I #4 Nov 30 2017 06:26:18
%S 1,2,2,3,8,3,4,15,15,4,6,33,41,33,6,9,104,120,120,104,9,13,228,465,
%T 534,465,228,13,19,529,1472,2976,2976,1472,529,19,28,1469,4667,13759,
%U 29081,13759,4667,1469,28,41,3442,16230,65009,187960,187960,65009,16230,3442
%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1s.
%C Table starts
%C ..1....2.....3.......4........6..........9..........13............19
%C ..2....8....15......33......104........228.........529..........1469
%C ..3...15....41.....120......465.......1472........4667.........16230
%C ..4...33...120.....534.....2976......13759.......65009........325008
%C ..6..104...465....2976....29081.....187960.....1311947......10551008
%C ..9..228..1472...13759...187960....1806751....18443146.....209884397
%C .13..529..4667...65009..1311947...18443146...279143247....4651767361
%C .19.1469.16230..325008.10551008..209884397..4651767361..117889600265
%C .28.3442.53266.1565481.75078015.2194039726.71601077879.2659460386138
%H R. H. Hardin, <a href="/A295943/b295943.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-3)
%F k=2: a(n) = a(n-1) +a(n-2) +9*a(n-3) -4*a(n-4) -4*a(n-5) -4*a(n-6)
%F k=3: [order 9]
%F k=4: [order 21]
%F k=5: [order 55]
%e Some solutions for n=5 k=4
%e ..1..0..0..0. .1..0..0..0. .1..1..0..1. .0..1..0..0. .1..0..0..0
%e ..0..1..1..1. .1..0..0..0. .1..1..0..1. .1..0..0..0. .1..0..0..1
%e ..0..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
%e ..1..0..0..1. .0..0..1..0. .0..0..0..0. .0..0..0..0. .0..1..0..0
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..1..0..0
%Y Column 1 is A000930(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 30 2017
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