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 A299740 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero. 7

%I #4 Feb 18 2018 10:16:09

%S 1,2,2,4,8,4,8,32,32,8,16,128,220,128,16,32,512,1578,1578,512,32,64,

%T 2048,11303,21111,11303,2048,64,128,8192,81105,280642,280642,81105,

%U 8192,128,256,32768,582032,3742524,6896530,3742524,582032,32768,256,512,131072

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 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......32.......128..........512...........2048.............8192

%C ...4....32.....220......1578........11303..........81105...........582032

%C ...8...128....1578.....21111.......280642........3742524.........49914496

%C ..16...512...11303....280642......6896530......170243005.......4203272237

%C ..32..2048...81105...3742524....170243005.....7790212998.....356575568843

%C ..64..8192..582032..49914496...4203272237...356575568843...30260326859957

%C .128.32768.4177161.665759775.103785926879.16322570202905.2568233775595684

%H R. H. Hardin, <a href="/A299740/b299740.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)

%F k=3: [order 8]

%F k=4: [order 24]

%F k=5: [order 79]

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A004171(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 18 2018

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Last modified September 23 09:36 EDT 2023. Contains 365544 sequences. (Running on oeis4.)