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A230469 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero 13

%I

%S 0,0,0,0,0,0,0,0,2,0,0,36,114,8,0,0,216,2398,1384,30,0,0,1260,35052,

%T 76518,16926,108,0,0,6912,552720,3062214,2593962,212124,386,0,0,38340,

%U 8724560,131421154,281740616,89087722,2647098,1376,0,0,213192,138661614

%N T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero

%C Table starts

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

%C .0....0........0...........36.............216...............1260

%C .0....2......114.........2398...........35052.............552720

%C .0....8.....1384........76518.........3062214..........131421154

%C .0...30....16926......2593962.......281740616........33169633760

%C .0..108...212124.....89087722.....26096227960......8449174734112

%C .0..386..2647098...3045192312...2412390974650...2147475302085202

%C .0.1376.33046400.104165339046.223089594072370.545932535826768684

%H R. H. Hardin, <a href="/A230469/b230469.txt">Table of n, a(n) for n = 1..126</a>

%F Empirical for column k:

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

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

%F k=3: [order 7]

%F k=4: [order 21]

%F k=5: [order 68]

%F Empirical for row n:

%F n=1: a(n) = a(n-1)

%F n=2: a(n) = 6*a(n-1) -a(n-2) -12*a(n-3) +20*a(n-4) +24*a(n-5)

%F n=3: [order 16] for n>17

%F n=4: [order 57] for n>58

%e Some solutions for n=3 k=4

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

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

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

%Y Column 2 is A230269

%K nonn,tabl

%O 1,9

%A _R. H. Hardin_, Oct 20 2013

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Last modified August 8 21:07 EDT 2022. Contains 356016 sequences. (Running on oeis4.)