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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.
5
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 12 2014
STATUS
approved