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

%I #4 Feb 27 2018 12:32:41

%S 1,2,2,4,8,4,8,32,32,8,16,128,255,128,16,32,512,2033,2033,512,32,64,

%T 2048,16208,32321,16208,2048,64,128,8192,129217,513832,513832,129217,

%U 8192,128,256,32768,1030173,8168705,16288960,8168705,1030173,32768,256,512,131072

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

%C Table starts

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

%C ...2......8.......32.........128............512.............2048

%C ...4.....32......255........2033..........16208...........129217

%C ...8....128.....2033.......32321.........513832..........8168705

%C ..16....512....16208......513832.......16288960........516368256

%C ..32...2048...129217.....8168705......516368256......32640586945

%C ..64...8192..1030173...129863167....16369174784....2063278351093

%C .128..32768..8212978..2064518282...518912313824..130424025161538

%C .256.131072.65477359.32820974441.16449820393120.8244367994118153

%H R. H. Hardin, <a href="/A300182/b300182.txt">Table of n, a(n) for n = 1..364</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: a(n) = 7*a(n-1) +7*a(n-2) +6*a(n-3)

%F k=4: a(n) = 14*a(n-1) +27*a(n-2) +51*a(n-3) -10*a(n-4) -a(n-5) -10*a(n-6)

%F k=5: [order 9]

%F k=6: [order 15]

%F k=7: [order 36]

%e Some solutions for n=5 k=4

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

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

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

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

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

%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 27 2018

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Last modified September 20 16:06 EDT 2024. Contains 376074 sequences. (Running on oeis4.)