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%I #4 Mar 10 2018 10:40:46
%S 0,0,0,0,1,0,0,2,2,0,0,4,2,4,0,0,9,10,10,9,0,0,19,30,64,30,19,0,0,41,
%T 104,316,316,104,41,0,0,88,340,1789,2998,1789,340,88,0,0,189,1144,
%U 9738,28089,28089,9738,1144,189,0,0,406,3795,54293,268615,456649,268615,54293,3795
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .0...0....0......0........0..........0............0..............0
%C .0...1....2......4........9.........19...........41.............88
%C .0...2....2.....10.......30........104..........340...........1144
%C .0...4...10.....64......316.......1789.........9738..........54293
%C .0...9...30....316.....2998......28089.......268615........2552014
%C .0..19..104...1789....28089.....456649......7455411......121708555
%C .0..41..340...9738...268615....7455411....209156119.....5850560104
%C .0..88.1144..54293..2552014..121708555...5850560104...280782187131
%C .0.189.3795.300456.24338903.1990954802.164070075524.13506744672543
%H R. H. Hardin, <a href="/A300646/b300646.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3)
%F k=3: [order 15]
%F k=4: [order 49]
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1
%e ..0..0..1..1. .0..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..1
%e ..0..1..0..0. .0..1..0..0. .1..1..1..1. .1..1..0..0. .0..0..1..0
%e ..1..1..0..0. .0..0..0..1. .1..0..1..1. .0..0..1..1. .1..1..0..0
%e ..1..0..0..0. .0..0..1..1. .0..0..1..1. .0..1..1..1. .1..0..0..0
%Y Column 2 is A078039(n-2).
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Mar 10 2018
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