cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A198914 T(n,k) = number of n X k 0..7 arrays with values 0..7 introduced in row major order and no element equal to any horizontal or vertical neighbor.

Original entry on oeis.org

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 500, 2051, 500, 15, 52, 10867, 269940, 269940, 10867, 52, 203, 313132, 54381563, 319608038, 54381563, 313132, 203, 877, 10856948, 13088156547, 481871809749, 481871809749, 13088156547, 10856948, 877, 4139
Offset: 1

Views

Author

R. H. Hardin, Oct 31 2011

Keywords

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 8 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
.....1............1..................2......................5
.....1............4.................34....................500
.....2...........34...............2051.................269940
.....5..........500.............269940..............319608038
....15........10867...........54381563...........481871809749
....52.......313132........13088156547........769126451071174
...203.....10856948......3352514013159....1243368053336112649
...877....418689772....876632051686733.2015791720035206825303
..4139..17067989413.230783525290600476
.21110.715189507700
...
Some solutions with values 0 to 7 for n=5, k=3:
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..1..2..1....1..0..1....1..2..1....1..0..2....1..0..2....1..2..3....1..2..3
..3..0..2....2..3..4....3..4..2....3..4..5....3..4..5....0..1..4....0..4..5
..2..4..5....5..4..3....5..6..1....5..3..6....6..7..0....5..6..7....1..5..1
..1..6..7....6..0..7....6..7..2....7..4..2....3..0..3....7..0..5....6..7..4

Links

Crossrefs

Columns 1-7 are A099262(n-1), A198908, A198909, A198910, A198911, A198912, A198913.
Main diagonal is A198907.
Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A222462 (labeled 8 colorings), A207868 (unlimited).

A214238 T(n,k) = Number of 0..7 colorings of an nx(k+1) array circular in the k+1 direction with new values 0..7 introduced in row major order.

Original entry on oeis.org

1, 1, 4, 4, 18, 34, 11, 354, 1067, 500, 41, 7749, 175884, 133265, 10867, 162, 231799, 35910351, 188834753, 24424881, 313132, 715, 8178855, 8769708263, 283323771619, 253155125338, 5178830173, 10856948, 3424, 318511707, 2254551356877
Offset: 1

Views

Author

R. H. Hardin, Jul 08 2012

Keywords

Comments

Table starts
.....1........1............4...............11...................41
.....4.......18..........354.............7749...............231799
....34.....1067.......175884.........35910351...........8769708263
...500...133265....188834753.....283323771619......454598044684573
.10867.24424881.253155125338.2440058302217191.24340562361200808002

Examples

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

Links

Crossrefs

Column 1 is A198908.
Showing 1-2 of 2 results.

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