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.

Showing 1-3 of 3 results.

A207868 T(n,k)=Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 500, 2052, 500, 15, 52, 10900, 278982, 278982, 10900, 52, 203, 322768, 68162042, 455546040, 68162042, 322768, 203, 877, 12297768, 26419793726, 1625686993918, 1625686993918, 26419793726, 12297768, 877
Offset: 1

Views

Author

R. H. Hardin, Feb 21 2012

Keywords

Comments

Table starts
...1.........1..............2.................5.................15
...1.........4.............34...............500..............10900
...2........34...........2052............278982...........68162042
...5.......500.........278982.........455546040......1625686993918
..15.....10900.......68162042.....1625686993918.103204230192540988
..52....322768....26419793726.10764437129618296
.203..12297768.15002771641712
.877.580849872

Examples

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

Links

Crossrefs

Columns 1..5 are A000110(n-1), A207864, A207865, A207866, A207867.
Main diagonal is A207863.
Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings).
Cf. A207981, A208001 (knight), A208021 (king), A208054, A208096, A208301.

A208096 T(n,k)=Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 1, 2, 2, 4, 5, 5, 30, 34, 15, 15, 377, 1573, 500, 52, 52, 7239, 169064, 192328, 10900, 203, 203, 193228, 34438557, 235862938, 43366459, 322768, 877, 877, 6752442, 11535531783, 677352910013, 746823293346, 15769674462, 12297768, 4140
Offset: 1

Views

Author

R. H. Hardin, Feb 23 2012

Keywords

Examples

			Table starts
....1........1...........2............5...........15..........52...........203
....2........4..........30..........377.........7239......193228.......6752442
....5.......34........1573.......169064.....34438557.11535531783.5804338800147
...15......500......192328....235862938.677352910013
...52....10900....43366459.746823293346
..203...322768.15769674462
..877.12297768
.4140
Some solutions for n=4 k=3
..0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..0....0..1..0
..0..1..2....2..1..0....0..1..0....0..3..2....0..3..0....2..3..0....0..1..0
..0..1..0....3..1..2....2..1..0....0..1..0....0..1..0....0..3..0....2..1..2
..0..1..0....2..1..0....2..1..2....3..1..0....0..3..0....0..1..0....0..1..0

Links

Crossrefs

Columns 1..5 are A000110, A207864, A208093, A208094, A208095.
Rows 1..5 are A000110(n-1), A208097, A208098, A208099, A208100.
Main diagonal is A361449.
Cf. A207868.

A216760 T(n,k)=Number of horizontal, vertical, diagonal, antidiagonal or knight-move neighbor colorings of an nXk array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 5, 4, 4, 5, 15, 34, 60, 34, 15, 52, 500, 2957, 2957, 500, 52, 203, 10900, 337731, 1340534, 337731, 10900, 203, 877, 322768, 71786149, 1842474893, 1842474893, 71786149, 322768, 877, 4140, 12297768, 24889021634
Offset: 1

Views

Author

R. H. Hardin Sep 15 2012

Keywords

Comments

Table starts
...1......1........2..........5.........15.......52.........203......877.4140
...1......1........4.........34........500....10900......322768.12297768
...2......4.......60.......2957.....337731.71786149.24889021634
...5.....34.....2957....1340534.1842474893
..15....500...337731.1842474893
..52..10900.71786149
.203.322768
.877

Examples

			Some solutions for n=3 k=4
..0..2..5..6....0..3..0..2....0..3..2..3....0..3..6..3....0..3..5..0
..1..3..1..3....1..4..6..4....1..4..5..6....1..4..1..2....1..4..1..2
..0..4..0..4....2..5..7..8....2..3..2..3....2..5..0..7....2..3..5..6

Crossrefs

Column 1 is A000110(n-1)
Column 2 is A207864(n-1)
Showing 1-3 of 3 results.

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