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T(n,k)=Number of nXk 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order
14

%I #4 Apr 20 2014 12:04:10

%S 1,1,2,2,7,5,4,28,47,14,8,121,460,326,41,16,523,4617,7376,2284,122,32,

%T 2261,46245,169982,118488,16026,365,64,9775,463567,3910194,6280325,

%U 1904096,112458,1094,128,42261,4646421,90008909,332185927,232173463

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order

%C Table starts

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

%C ....2.......7.........28............121...............523.................2261

%C ....5......47........460...........4617.............46245...............463567

%C ...14.....326.......7376.........169982...........3910194.............90008909

%C ...41....2284.....118488........6280325.........332185927..........17583615124

%C ..122...16026....1904096......232173463.......28238828935........3437694358689

%C ..365..112458...30598800.....8582759752.....2400505507498......672068364873884

%C .1094..789166..491723328...317280724429...204061855414167...131390467341043995

%C .3281.5537942.7902006144.11729003927933.17346886991310331.25687100469219790719

%H R. H. Hardin, <a href="/A241370/b241370.txt">Table of n, a(n) for n = 1..144</a>

%F Empirical for column k:

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

%F k=2: a(n) = 7*a(n-1) +2*a(n-3) -8*a(n-4) for n>5

%F k=3: [order 8]

%F k=4: [order 31]

%F k=5: [order 94]

%F Empirical for row n:

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

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

%F n=3: a(n) = 9*a(n-1) +16*a(n-2) -50*a(n-3) -72*a(n-4) -32*a(n-5) -32*a(n-6) for n>8

%F n=4: [order 21] for n>23

%F n=5: [order 65] for n>67

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A007051(n-1)

%Y Row 1 is A000079(n-2)

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Apr 20 2014