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A317741 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 8

%I

%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,4,3,3,4,0,0,9,2,4,2,9,0,0,22,4,14,14,

%T 4,22,0,0,53,6,23,14,23,6,53,0,0,130,14,35,38,38,35,14,130,0,0,320,14,

%U 98,74,22,74,98,14,320,0,0,788,22,213,149,36,36,149,213,22,788,0,0,1942,43

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

%C Table starts

%C .0...0..0...0...0...0....0...0....0....0.....0.....0.....0......0......0

%C .0...1..1...2...4...9...22..53..130..320...788..1942..4787..11801..29093

%C .0...1..1...3...2...4....6..14...14...22....43....68....82....147....246

%C .0...2..3...4..14..23...35..98..213..448..1053..2285..5170..11442..25631

%C .0...4..2..14..14..38...74.149..269..662..1294..2721..5911..12084..25175

%C .0...9..4..23..38..22...36.140..146..218...736..1072..1890...4505...8860

%C .0..22..6..35..74..36..274.280.1065.1939..5947.13101.35847..83062.222994

%C .0..53.14..98.149.140..280.676..914.2388..3845.11110.14133..42876..69411

%C .0.130.14.213.269.146.1065.914.3242.5466.15470.37531.94202.234901.706951

%H R. H. Hardin, <a href="/A317741/b317741.txt">Table of n, a(n) for n = 1..645</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) -a(n-6)

%F k=3: [order 10] for n>13

%F k=4: [order 23] for n>26

%F k=5: [order 33] for n>39

%F k=6: [order 56] for n>63

%F k=7: [order 97] for n>108

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Aug 05 2018

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Last modified June 27 16:27 EDT 2022. Contains 354896 sequences. (Running on oeis4.)