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A318552 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 0,1,1,1,3,1,2,6,6,2,3,10,5,10,3,5,21,21,21,21,5,8,46,44,64,44,46,8,

%T 13,102,106,219,219,106,102,13,21,220,258,589,842,589,258,220,21,34,

%U 491,600,1782,3172,3172,1782,600,491,34,55,1077,1476,5621,12073,14760,12073,5621

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 6 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...3....6....10.....21......46......102.......220........491........1077

%C ..1...6....5....21.....44.....106......258.......600.......1476........3461

%C ..2..10...21....64....219.....589.....1782......5621......17333.......54199

%C ..3..21...44...219....842....3172....12073.....49181.....191426......766695

%C ..5..46..106...589...3172...14760....67976....337349....1614708.....7855731

%C ..8.102..258..1782..12073...67976...437825...2689769...16069287...100151409

%C .13.220..600..5621..49181..337349..2689769..21556643..159367978..1242485030

%C .21.491.1476.17333.191426.1614708.16069287.159367978.1516492860.14741167613

%H R. H. Hardin, <a href="/A318552/b318552.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) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

%F k=3: [order 31]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A317857.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 28 2018

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)