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%I #4 Mar 10 2018 10:32:13
%S 0,1,1,1,2,1,2,6,6,2,3,15,13,15,3,5,37,34,34,37,5,8,90,91,97,91,90,8,
%T 13,223,253,300,300,253,223,13,21,550,705,1036,1130,1036,705,550,21,
%U 34,1355,1978,3313,4418,4418,3313,1978,1355,34,55,3341,5507,11075,17607,23097
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..0....1....1.....2......3.......5........8........13.........21..........34
%C ..1....2....6....15.....37......90......223.......550.......1355........3341
%C ..1....6...13....34.....91.....253......705......1978.......5507.......15222
%C ..2...15...34....97....300....1036.....3313.....11075......37067......122922
%C ..3...37...91...300...1130....4418....17607.....71861.....297729.....1239693
%C ..5...90..253..1036...4418...23097...124439....666648....3654138....20086516
%C ..8..223..705..3313..17607..124439...865205...6105466...44264248...319622847
%C .13..550.1978.11075..71861..666648..6105466..57365508..551242313..5228508530
%C .21.1355.5507.37067.297729.3654138.44264248.551242313.7042663221.88534058107
%H R. H. Hardin, <a href="/A300639/b300639.txt">Table of n, a(n) for n = 1..220</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) +3*a(n-3) +2*a(n-4) +a(n-5)
%F k=3: [order 32]
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..0..1..1. .0..0..1..1. .0..1..1..1. .0..0..0..1
%e ..0..0..0..1. .1..0..0..1. .0..1..0..1. .0..0..0..1. .1..1..0..1
%e ..1..1..1..1. .1..1..0..1. .1..0..0..0. .1..1..0..1. .0..1..0..1
%e ..0..0..1..1. .0..1..0..1. .0..0..0..1. .1..0..1..0. .0..0..1..0
%e ..1..1..0..0. .0..1..0..1. .1..1..0..1. .0..1..0..0. .1..1..0..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A300344.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Mar 10 2018
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