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%I #4 Mar 09 2018 17:35:39
%S 0,1,1,1,3,1,2,10,10,2,3,30,53,30,3,5,96,277,277,96,5,8,307,1432,2347,
%T 1432,307,8,13,981,7514,19532,19532,7514,981,13,21,3137,39330,164619,
%U 263468,164619,39330,3137,21,34,10034,205958,1387896,3567928,3567928
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1.......1........2..........3............5..............8
%C ..1.....3......10.......30.........96..........307............981
%C ..1....10......53......277.......1432.........7514..........39330
%C ..2....30.....277.....2347......19532.......164619........1387896
%C ..3....96....1432....19532.....263468......3567928.......48279880
%C ..5...307....7514...164619....3567928.....77669371.....1693172810
%C ..8...981...39330..1387896...48279880...1693172810....59556673490
%C .13..3137..205958.11697909..653282566..36914891724..2093683166397
%C .21.10034.1078479.98591087.8839456244.804586936082.73570793306416
%H R. H. Hardin, <a href="/A300612/b300612.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6) for n>7
%F k=3: [order 17] for n>18
%F k=4: [order 72] for n>73
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..1..1..0. .0..0..0..1. .0..1..0..0. .0..0..0..0
%e ..0..1..0..1. .0..1..0..0. .1..0..0..1. .0..1..1..0. .0..1..1..0
%e ..0..1..0..1. .1..0..1..0. .1..1..0..0. .0..0..1..1. .0..0..1..1
%e ..0..1..0..0. .1..0..1..0. .1..0..1..0. .0..1..0..1. .1..0..0..1
%e ..1..0..1..1. .0..0..0..0. .0..1..1..0. .1..1..0..0. .1..1..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A300421.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 09 2018
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