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 A305692 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7

%I

%S 0,1,1,1,7,1,2,25,25,2,3,98,152,98,3,5,383,1151,1151,383,5,8,1493,

%T 8415,16658,8415,1493,8,13,5824,61796,236246,236246,61796,5824,13,21,

%U 22717,453553,3346848,6433903,3346848,453553,22717,21,34,88609,3329201

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0.....1........1..........2.............3................5..................8

%C ..1.....7.......25.........98...........383.............1493...............5824

%C ..1....25......152.......1151..........8415............61796.............453553

%C ..2....98.....1151......16658........236246..........3346848...........47448563

%C ..3...383.....8415.....236246.......6433903........175572754.........4791219558

%C ..5..1493....61796....3346848.....175572754.......9226209199.......484920924010

%C ..8..5824...453553...47448563....4791219558.....484920924010.....49083436693252

%C .13.22717..3329201..672609073..130750175963...25486278629503...4968168200482612

%C .21.88609.24436772.9534641574.3568076221953.1339494303168987.502868587709213674

%H R. H. Hardin, <a href="/A305692/b305692.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 6*a(n-1) +8*a(n-2) +12*a(n-3) +11*a(n-4) -a(n-5) +a(n-6) +a(n-7) -a(n-8)

%F k=4: [order 17]

%F k=5: [order 52]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304421.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jun 08 2018

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Last modified March 24 18:32 EDT 2023. Contains 361510 sequences. (Running on oeis4.)