A238912 - OEIS

%I #4 Mar 07 2014 07:05:15

%S 3,9,9,54,41,54,261,486,486,261,1341,4287,17496,4287,1341,6768,41165,

%T 408726,408726,41165,6768,34335,385632,10789686,22778013,10789686,

%U 385632,34335,173925,3638773,274834944,1474369337,1474369337,274834944,3638773

%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..2 introduced in row major order

%C Table starts

%C .......3..........9..............54.................261....................1341

%C .......9.........41.............486................4287...................41165

%C ......54........486...........17496..............408726................10789686

%C .....261.......4287..........408726............22778013..............1474369337

%C ....1341......41165........10789686..........1474369337............241302194385

%C ....6768.....385632.......274834944.........91433307852..........37515316223070

%C ...34335....3638773......7073353350.......5739848041311........5917999098852871

%C ..173925...34262775....181499433750.....359075051396597......929709624020566839

%C ..881406..322817734...4661259221016...22485455035768752...146227628520093446270

%C .4466169.3040984385.119679993219366.1407650415969195223.22991463214552411818739

%H R. H. Hardin, <a href="/A238912/b238912.txt">Table of n, a(n) for n = 1..111</a>

%F Empirical for column k:

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

%F k=2: [order 10]

%F k=3: a(n) = 22*a(n-1) +120*a(n-2) -678*a(n-3) +522*a(n-4) +432*a(n-5) -81*a(n-6)

%e Some solutions for n=3 k=4

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 07 2014