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A317118 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 1,2,2,4,8,4,8,30,30,8,16,112,142,112,16,32,420,698,698,420,32,64,

%T 1576,3398,5157,3398,1576,64,128,5912,16686,37221,37221,16686,5912,

%U 128,256,22176,81809,273221,392393,273221,81809,22176,256,512,83184,401415

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1.....2.......4.........8.........16...........32.............64

%C ...2.....8......30.......112........420.........1576...........5912

%C ...4....30.....142.......698.......3398........16686..........81809

%C ...8...112.....698......5157......37221.......273221........2000595

%C ..16...420....3398.....37221.....392393......4237829.......45938893

%C ..32..1576...16686....273221....4237829.....67247490.....1080066752

%C ..64..5912...81809...2000595...45938893...1080066752....25956605294

%C .128.22176..401415..14657917..497129492..17278502991...620005212254

%C .256.83184.1969107.107409094.5387633738.277268412729.14887658798448

%H R. H. Hardin, <a href="/A317118/b317118.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 10] for n>12

%F k=4: [order 35] for n>37

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A281949.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 21 2018

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)