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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A216460 T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 7, 5, 5, 2, 5, 15, 20, 15, 5, 5, 15, 203, 203, 322, 52, 15, 5, 52, 716, 3429, 4140, 1335, 203, 15, 15, 203, 17733, 83440, 580479, 115975, 36401, 877, 52, 15, 877, 83440, 2711768, 18171918, 20880505, 4213597, 192713, 4140, 52, 52
Offset: 1

Views

Author

R. H. Hardin Sep 07 2012

Keywords

Comments

Table starts
...1......1..........1............1...............2................2
...1......1..........1............2...............5...............15
...2......2..........7...........15.............203..............716
...2......5.........20..........203............3429............83440
...5.....15........322.........4140..........580479.........18171918
...5.....52.......1335.......115975........20880505.......6423127757
..15....203......36401......4213597......8195008751....3376465219485
..15....877.....192713....190899322....484968748793.2486327138729353
..52...4140....7712455..10480142147.348950573407587
..52..21147...49055292.682076806159
.203.115975.2659544320
.203.678570

Examples

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

Links

Crossrefs

Column 2 is A000110(n-1)
Column 4 is A020557(n-1)
Column 6 is A208051
Row 2 is A000110(n-2)
Odd squares: A216612

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.

Original entry on oeis.org

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

Views

Author

R. H. Hardin Sep 10 2012

Keywords

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

Examples

			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

Links

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

A208054 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, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 5, 15, 15, 5, 15, 203, 716, 203, 15, 52, 4140, 83440, 83440, 4140, 52, 203, 115975, 18171918, 112073062, 18171918, 115975, 203, 877, 4213597, 6423127757, 346212384169, 346212384169, 6423127757, 4213597, 877, 4140, 190899322
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Equivalently, the number of colorings in the rhombic hexagonal square grid graph RH_(n,k) using any number of colors up to permutation of the colors. - Andrew Howroyd, Jun 25 2017

Examples

			Table starts
...1.........1.............2................5................15
...1.........2............15..............203..............4140
...2........15...........716............83440..........18171918
...5.......203.........83440........112073062......346212384169
..15......4140......18171918.....346212384169.18633407199331522
..52....115975....6423127757.2043836452962923
.203...4213597.3376465219485
.877.190899322
...
Some solutions for n=4 k=3
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0
..2..3..1....2..3..4....2..3..2....2..3..1....2..3..0....2..3..1....2..3..2
..4..2..4....0..5..0....0..4..0....0..4..5....4..5..3....4..5..3....0..1..4
..0..5..0....1..2..1....1..2..1....5..3..4....0..1..0....0..6..4....2..0..1

Links

Crossrefs

Columns 1-5 are A000110(n-1), A020557(n-1), A208051, A208052, A208053.
Cf. A207868, A212162, A212163, A208050, A068271.
Showing 1-3 of 3 results.

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