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A298139 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 7 king-move adjacent elements, with upper left element zero. 6

%I

%S 0,0,0,0,1,0,0,3,3,0,0,2,0,2,0,0,11,3,3,11,0,0,13,0,10,0,13,0,0,34,3,

%T 20,20,3,34,0,0,65,6,68,88,68,6,65,0,0,123,23,185,242,242,185,23,123,

%U 0,0,266,68,561,627,917,627,561,68,266,0,0,499,205,1600,2604,3417,3417,2604

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

%C Table starts

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

%C .0...1..3....2...11....13.....34......65......123.......266.......499

%C .0...3..0....3....0.....3......6......23.......68.......205.......572

%C .0...2..3...10...20....68....185.....561.....1600......4856.....14490

%C .0..11..0...20...88...242....627....2604.....8137.....28727....101137

%C .0..13..3...68..242...917...3417...14533....58845....244155...1024766

%C .0..34..6..185..627..3417..14422...73961...354200...1772595...8807624

%C .0..65.23..561.2604.14533..73961..467043..2633905..15796516..93682029

%C .0.123.68.1600.8137.58845.354200.2633905.17828062.127068717.899366629

%H R. H. Hardin, <a href="/A298139/b298139.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) = a(n-1) +3*a(n-2) -4*a(n-4)

%F k=3: [order 17] for n>18

%F k=4: [order 60] for n>61

%e Some solutions for n=7 k=4

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

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

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

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

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

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

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

%Y Column 2 is A297870.

%Y Column 3 is A297871.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Jan 13 2018

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Last modified September 22 19:36 EDT 2021. Contains 347608 sequences. (Running on oeis4.)