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A300923 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 1,1,1,1,3,1,1,5,5,1,1,16,20,16,1,1,40,76,76,40,1,1,113,290,593,290,

%T 113,1,1,304,1245,4066,4066,1245,304,1,1,833,5160,30474,48588,30474,

%U 5160,833,1,1,2270,21819,224767,640673,640673,224767,21819,2270,1,1,6194,91713

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C .1....1.....1........1..........1............1..............1................1

%C .1....3.....5.......16.........40..........113............304..............833

%C .1....5....20.......76........290.........1245...........5160............21819

%C .1...16....76......593.......4066........30474.........224767..........1677576

%C .1...40...290.....4066......48588.......640673........8265835........108469760

%C .1..113..1245....30474.....640673.....14914968......340365586.......7878577344

%C .1..304..5160...224767....8265835....340365586....13715723327.....560932609225

%C .1..833.21819..1677576..108469760...7878577344...560932609225...40555879417852

%C .1.2270.91713.12501697.1419225976.181974865532.22881004568048.2924437698122344

%H R. H. Hardin, <a href="/A300923/b300923.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 21] for n>22

%F k=4: [order 66] for n>68

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A300533.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 15 2018

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Last modified August 19 05:01 EDT 2022. Contains 356216 sequences. (Running on oeis4.)