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A320371 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 1,2,2,4,8,4,8,32,32,8,16,128,228,128,16,32,512,1612,1612,512,32,64,

%T 2048,11396,19840,11396,2048,64,128,8192,80568,245060,245060,80568,

%U 8192,128,256,32768,569608,3027408,5304988,3027408,569608,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1......2........4..........8............16..............32................64

%C ...2......8.......32........128...........512............2048..............8192

%C ...4.....32......228.......1612.........11396...........80568............569608

%C ...8....128.....1612......19840........245060.........3027408..........37398884

%C ..16....512....11396.....245060.......5304988.......114844160........2486026176

%C ..32...2048....80568....3027408.....114844160......4358279956......165355751224

%C ..64...8192...569608...37398884....2486026176....165355751224....10993944343316

%C .128..32768..4027076..462004160...53815748216...6274017360108...731023916987668

%C .256.131072.28471056.5707334644.1164968680976.238053099337172.48608312646628816

%H R. H. Hardin, <a href="/A320371/b320371.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1)

%F k=2: a(n) = 4*a(n-1)

%F k=3: a(n) = 8*a(n-1) -7*a(n-2) +3*a(n-3)

%F k=4: [order 9]

%F k=5: [order 25] for n>26

%F k=6: [order 70] for n>73

%e Some solutions for n=5 k=4

%e ..0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..1..0

%e ..0..0..1..1. .1..1..0..0. .1..1..1..1. .1..1..1..0. .0..0..0..1

%e ..1..1..0..0. .1..1..0..1. .0..1..1..1. .1..1..0..0. .0..0..1..1

%e ..1..0..0..0. .0..0..0..0. .0..0..0..1. .0..1..0..0. .0..1..0..1

%e ..1..1..1..0. .0..1..0..1. .1..0..0..0. .1..0..1..1. .1..0..0..0

%Y Column 1 is A000079(n-1).

%Y Column 2 is A004171(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Oct 11 2018

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Last modified September 28 17:43 EDT 2020. Contains 337393 sequences. (Running on oeis4.)