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A232335 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal 12

%I

%S 1,2,1,4,6,1,6,18,16,1,10,32,74,42,1,16,82,154,308,110,1,26,162,628,

%T 734,1282,288,1,42,388,1470,4906,3472,5338,754,1,68,806,5530,13170,

%U 38986,16338,22228,1974,1,110,1858,13906,82526,117690,312276,76630,92562,5168

%N T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal

%C Table starts

%C .1.....2.......4.......6.........10.........16............26............42

%C .1.....6......18......32.........82........162...........388...........806

%C .1....16......74.....154........628.......1470..........5530.........13906

%C .1....42.....308.....734.......4906......13170.........82526........239992

%C .1...110....1282....3472......38986.....117690.......1274656.......4158066

%C .1...288....5338...16338.....312276....1047700......20052758......71916112

%C .1...754...22228...76630....2510674....9298730.....318521414....1241196022

%C .1..1974...92562..358656...20221026...82332898....5084744564...21383016966

%C .1..5168..385450.1676330..162993780..727588212...81376107850..367791626696

%C .1.13530.1605108.7828014.1314329242.6419787202.1303994749578.6317140944234

%H R. H. Hardin, <a href="/A232335/b232335.txt">Table of n, a(n) for n = 1..448</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 5*a(n-1) -3*a(n-2) -2*a(n-3)

%F k=4: a(n) = 7*a(n-1) -9*a(n-2) -8*a(n-3) -4*a(n-4)

%F k=5: a(n) = 11*a(n-1) -21*a(n-2) -20*a(n-3) -12*a(n-4) for n>5

%F k=6: [order 7] for n>9

%F k=7: [order 16] for n>18

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2) for n>3

%F n=2: a(n) = a(n-1) +3*a(n-2) -a(n-3) +a(n-4) -a(n-5) for n>6

%F n=3: [order 8] for n>12

%F n=4: [order 21] for n>24

%F n=5: [order 36] for n>42

%F n=6: [order 80] for n>87

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A025169(n-1)

%Y Column 3 is A218059

%Y Row 1 is A006355(n+1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 22 2013

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Last modified September 25 15:27 EDT 2021. Contains 347658 sequences. (Running on oeis4.)