A238912 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

3, 9, 9, 54, 41, 54, 261, 486, 486, 261, 1341, 4287, 17496, 4287, 1341, 6768, 41165, 408726, 408726, 41165, 6768, 34335, 385632, 10789686, 22778013, 10789686, 385632, 34335, 173925, 3638773, 274834944, 1474369337, 1474369337, 274834944, 3638773

Offset

1,1

Comments

Table starts

.......3..........9..............54.................261....................1341

.......9.........41.............486................4287...................41165

......54........486...........17496..............408726................10789686

.....261.......4287..........408726............22778013..............1474369337

....1341......41165........10789686..........1474369337............241302194385

....6768.....385632.......274834944.........91433307852..........37515316223070

...34335....3638773......7073353350.......5739848041311........5917999098852871

..173925...34262775....181499433750.....359075051396597......929709624020566839

..881406..322817734...4661259221016...22485455035768752...146227628520093446270

.4466169.3040984385.119679993219366.1407650415969195223.22991463214552411818739

Links

R. H. Hardin, Table of n, a(n) for n = 1..111

Formula

Empirical for column k:

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

k=2: [order 10]

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)

Example

Some solutions for n=3 k=4
..0..1..0..1..2....0..1..0..0..1....0..1..0..1..0....0..1..0..1..0
..1..2..1..2..1....1..0..2..2..0....1..2..1..0..1....2..0..2..0..2
..0..2..0..2..0....0..1..2..1..0....0..2..1..0..2....0..2..1..1..2
..2..1..2..1..2....1..0..1..0..1....2..1..2..2..1....2..1..0..2..0

Crossrefs

Sequence in context: A203558 A223653 A351929 * A038227 A080292 A273893

Adjacent sequences: A238909 A238910 A238911 * A238913 A238914 A238915

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 07 2014

Status

approved