A240774 T(n,k) = Number of n X k 0..3 arrays with no element equal to exactly one horizontal or vertical neighbor, with new values 0..3 introduced in row major order.

1, 1, 1, 2, 5, 2, 5, 28, 28, 5, 14, 196, 475, 196, 14, 41, 1418, 8319, 8319, 1418, 41, 122, 10314, 147231, 357943, 147231, 10314, 122, 365, 75138, 2610234, 15484811, 15484811, 2610234, 75138, 365, 1094, 547557, 46306024, 671539712, 1641787181

Offset

1,4

Comments

Table starts

....1........1............2..............5...............14................41

....1........5...........28............196.............1418.............10314

....2.......28..........475...........8319...........147231...........2610234

....5......196.........8319.........357943.........15484811.........671539712

...14.....1418.......147231.......15484811.......1641787181......174833637032

...41....10314......2610234......671539712.....174833637032....45829139264557

..122....75138.....46306024....29164866719...18668613617376.12065218512657635

..365...547557....821735065..1267677501494.1996696858027452

.1094..3990640..14584690111.55127359226486

.3281.29085026.258881423308

Links

R. H. Hardin, Table of n, a(n) for n = 1..84

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -3*a(n-2) for n>3,

k=2: [order 10] for n>11,

k=3: [order 34] for n>35.

Example

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

Crossrefs

Column 1 is A007051(n-2).

Sequence in context: A269920 A240706 A240642 * A198604 A198253 A159989

Adjacent sequences: A240771 A240772 A240773 * A240775 A240776 A240777

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 12 2014

Status

approved