A216612 T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 5, 2, 2, 5, 15, 20, 15, 5, 2, 15, 41, 203, 67, 52, 5, 5, 52, 716, 3429, 4140, 1335, 203, 15, 5, 203, 2847, 83440, 83437, 115975, 6097, 877, 15, 15, 877, 83440, 2711768, 18171918, 20880505, 4213597, 192713, 4140, 52, 15, 4140

Offset

1,9

Comments

Table starts

...1......1.........1............1..............1................2

...1......1.........1............2..............5...............15

...1......2.........2...........15.............41..............716

...2......5........20..........203...........3429............83440

...2.....15........67.........4140..........83437.........18171918

...5.....52......1335.......115975.......20880505.......6423127757

...5....203......6097......4213597......942420901....3376465219485

..15....877....192713....190899322...484968748793.2486327138729353

..15...4140...1094076..10480142147.33862631596393

..52..21147..49055292.682076806159

..52.115975.329588907

.203.678570

Links

R. H. Hardin, Table of n, a(n) for n = 1..96

Example

Some solutions for n=4 k=4
..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
..2..x..3..x....2..x..3..x....1..x..2..x....2..x..3..x....1..x..2..x
..x..4..x..2....x..1..x..2....x..0..x..3....x..4..x..0....x..3..x..4
..5..x..6..x....4..x..3..x....2..x..1..x....2..x..5..x....0..x..2..x

Crossrefs

Column 2 is A000110(n-1)

Column 4 is A020557(n-1)

Column 6 is A208051

Row 2 is A000110(n-2)

Row 4 is A216462

Row 6 is A216464

Even squares: A216460

Sequence in context: A156748 A351455 A075445 * A194447 A307219 A345764

Adjacent sequences: A216609 A216610 A216611 * A216613 A216614 A216615

Keyword

nonn,tabl

Author

R. H. Hardin Sep 10 2012

Status

approved