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 A281129 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 6

%I #4 Jan 15 2017 07:39:37

%S 0,0,0,1,2,1,2,28,28,2,8,208,574,208,8,28,1364,5590,5590,1364,28,94,

%T 8354,48828,75668,48828,8354,94,304,48992,394202,923678,923678,394202,

%U 48992,304,960,278966,3042893,10441416,15835126,10441416,3042893,278966,960

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Table starts

%C ....0.......0..........1............2............8............28............94

%C ....0.......2.........28..........208.........1364..........8354.........48992

%C ....1......28........574.........5590........48828........394202.......3042893

%C ....2.....208.......5590........75668.......923678......10441416.....112649322

%C ....8....1364......48828.......923678.....15835126.....250872018....3803844412

%C ...28....8354.....394202.....10441416....250872018....5550177494..117185694820

%C ...94...48992....3042893....112649322...3803844412..117185694820.3459450309336

%C ..304..278966...22772368...1178277478..55967077710.2402634147622

%C ..960.1554744..166675727..12052427112.805490418258

%C .2976.8524848.1199580226.121217893114

%H R. H. Hardin, <a href="/A281129/b281129.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1) -8*a(n-3) -4*a(n-4) for n>7

%F k=2: a(n) = 8*a(n-1) -8*a(n-2) -30*a(n-3) -24*a(n-4) -8*a(n-5) -a(n-6)

%F k=3: [order 23] for n>30

%e Some solutions for n=4 k=4

%e ..0..1..1..0. .0..1..1..2. .0..0..1..2. .0..1..0..0. .0..0..1..2

%e ..0..2..2..1. .0..2..2..1. .1..2..0..2. .0..2..1..2. .2..2..0..1

%e ..1..0..1..0. .1..1..0..2. .0..2..0..1. .1..1..0..1. .0..1..2..2

%e ..2..2..1..0. .2..2..1..1. .1..0..1..2. .0..2..0..2. .2..1..0..2

%Y Column 1 is A280279.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 15 2017

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Last modified September 25 04:27 EDT 2023. Contains 365582 sequences. (Running on oeis4.)