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 A317871 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7

%I

%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,4,6,6,4,0,0,9,4,26,4,9,0,0,22,5,88,

%T 88,5,22,0,0,53,10,301,220,301,10,53,0,0,130,36,1089,759,759,1089,36,

%U 130,0,0,320,34,4340,3303,4692,3303,4340,34,320,0,0,788,43,16696,11807,27620

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 5 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

%C .0...1..1.....2.....4......9......22........53........130.........320

%C .0...1..1.....6.....4......5......10........36.........34..........43

%C .0...2..6....26....88....301....1089......4340......16696.......64514

%C .0...4..4....88...220....759....3303.....11807......45995......161983

%C .0...9..5...301...759...4692...27620....167100.....990871.....5767582

%C .0..22.10..1089..3303..27620..163297...1242087....7872632....53760082

%C .0..53.36..4340.11807.167100.1242087..13125877..113996501..1068543427

%C .0.130.34.16696.45995.990871.7872632.113996501.1146051177.13578301848

%H R. H. Hardin, <a href="/A317871/b317871.txt">Table of n, a(n) for n = 1..220</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 18]

%F k=4: [order 83] for n>86

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A317735.

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Aug 09 2018

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Last modified May 23 13:13 EDT 2019. Contains 323514 sequences. (Running on oeis4.)