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 A233018 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 in row major order 7

%I #4 Dec 03 2013 07:05:25

%S 1,2,2,5,11,5,14,74,74,14,41,515,1202,515,41,122,3602,19643,19643,

%T 3602,122,365,25211,321125,750092,321125,25211,365,1094,176474,

%U 5249894,28644884,28644884,5249894,176474,1094,3281,1235315,85827722,1093911305

%N T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 in row major order

%C Table starts

%C ....1.......2..........5............14...............41.................122

%C ....2......11.........74...........515.............3602...............25211

%C ....5......74.......1202.........19643...........321125.............5249894

%C ...14.....515......19643........750092.........28644884..........1093911305

%C ...41....3602.....321125......28644884.......2555361596........227962456547

%C ..122...25211....5249894....1093911305.....227962456547......47506658438246

%C ..365..176474...85827722...41775098873...20336458202315....9900284810558324

%C .1094.1235315.1403151863.1595338735322.1814209743962774.2063199965393914025

%H R. H. Hardin, <a href="/A233018/b233018.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 19*a(n-1) -45*a(n-2) +27*a(n-3)

%F k=4: a(n) = 46*a(n-1) -312*a(n-2) +530*a(n-3) -263*a(n-4)

%F k=5: [order 8]

%F k=6: [order 14]

%F k=7: [order 33]

%e Some solutions for n=3 k=4

%e ..0..1..1..1....0..0..1..3....0..1..1..1....0..1..3..1....0..0..0..1

%e ..1..1..1..1....0..1..3..1....1..1..3..1....1..3..2..0....2..0..2..0

%e ..0..1..1..0....0..1..3..3....1..1..3..3....1..1..3..1....0..0..2..2

%Y Column 1 is A007051(n-1)

%Y Column 2 is A199417(n-1)

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Dec 03 2013

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Last modified October 3 17:33 EDT 2023. Contains 365870 sequences. (Running on oeis4.)