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 1-10 of 18 results. Next

A207997 T(n,k) = number of n X k 0..2 arrays with new values 0..2 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, 3, 2, 4, 9, 9, 4, 8, 27, 41, 27, 8, 16, 81, 187, 187, 81, 16, 32, 243, 853, 1302, 853, 243, 32, 64, 729, 3891, 9075, 9075, 3891, 729, 64, 128, 2187, 17749, 63267, 96831, 63267, 17749, 2187, 128, 256, 6561, 80963, 441090, 1034073, 1034073, 441090, 80963
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 3 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
..1....1.....2.......4.........8.........16...........32............64
..1....3.....9......27........81........243..........729..........2187
..2....9....41.....187.......853.......3891........17749.........80963
..4...27...187....1302......9075......63267.......441090.......3075255
..8...81...853....9075.....96831....1034073.....11045757.....117997043
.16..243..3891...63267...1034073...16932816....277458045....4547477370
.32..729.17749..441090..11045757..277458045...6978332618..175605187731
.64.2187.80963.3075255.117997043.4547477370.175605187731.6787438272198
...
Some solutions for n=4, k=3:
..0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0
..2..0..1....2..0..2....1..0..2....1..2..1....2..0..1....1..2..1....1..2..1
..0..2..0....0..1..0....2..1..0....0..1..2....0..2..0....0..1..2....2..0..2
..1..0..1....1..2..1....1..0..1....1..2..0....2..0..2....2..0..1....1..2..0

Links

Crossrefs

Cf. A020698 (column 3), A078100 (column 4), A207994 (column 5), A207995 (column 6), A207996 (column 7).
Main diagonal is A207993.
Cf. A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

Formula

2*T(n,m) = A078099(n,m) for m>1. - R. J. Mathar, Nov 23 2015

A198715 T(n,k)=Number of nXk 0..3 arrays with values 0..3 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, 25, 25, 5, 14, 172, 401, 172, 14, 41, 1201, 6548, 6548, 1201, 41, 122, 8404, 107042, 250031, 107042, 8404, 122, 365, 58825, 1749965, 9548295, 9548295, 1749965, 58825, 365, 1094, 411772, 28609241, 364637102, 851787199, 364637102
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2011

Keywords

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 4 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
....1........1............2...............5..................14
....1........4...........25.............172................1201
....2.......25..........401............6548..............107042
....5......172.........6548..........250031.............9548295
...14.....1201.......107042.........9548295...........851787199
...41.....8404......1749965.......364637102.........75987485516
..122....58825.....28609241.....13925032958.......6778819400772
..365...411772....467717288....531779578441.....604736581320925
.1094..2882401...7646461682..20307996787865...53948385378521909
.3281.20176804.125007943505.775536991678112.4812720805166620356
...
Some solutions with all values from 0 to 3 for n=6 k=4
..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..0....1..0..1..0....1..0..1..0....1..0..1..0
..0..1..2..1....0..1..0..1....0..1..0..1....0..1..0..2....0..1..0..1
..1..2..0..3....2..0..3..0....2..0..1..0....1..2..1..3....1..2..3..0
..2..0..2..0....1..3..0..2....3..2..0..2....0..3..0..2....3..1..2..3
..3..2..0..1....3..2..1..0....0..3..2..1....3..1..3..0....1..3..1..0

Links

Crossrefs

Columns 1-7 are A007051(n-2), A034494(n-1), A198710, A198711, A198712, A198713, A198714.
Main diagonal is A198709.
Cf. A207997 (3 colorings), A222444 (labeled 4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

A198906 T(n,k) = number of n X k 0..4 arrays with values 0..4 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, 33, 33, 5, 15, 380, 1211, 380, 15, 51, 4801, 50384, 50384, 4801, 51, 187, 62004, 2125425, 6907736, 2125425, 62004, 187, 715, 804833, 89793204, 948656912, 948656912, 89793204, 804833, 715, 2795, 10459180, 3794115705
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 5 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
.....1..........1...............2....................5
.....1..........4..............33..................380
.....2.........33............1211................50384
.....5........380...........50384..............6907736
....15.......4801.........2125425............948656912
....51......62004........89793204.........130292546801
...187.....804833......3794115705.......17895005957823
...715...10459180....160319061892.....2457786852894234
..2795..135958401...6774239755817...337564362706067534
.11051.1767426404.286243775060868.46362726246946052884
...
Some solutions with values 0 to 4 for n=6, k=4:
..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..0....1..0..1..0....1..0..1..0....1..0..1..0
..0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2
..2..0..2..0....2..0..3..0....2..0..2..3....2..0..1..0....2..0..1..3
..3..2..1..4....0..1..0..4....0..4..0..2....3..2..4..3....0..3..4..2
..2..4..2..1....2..4..3..1....1..3..1..4....1..0..1..2....4..0..1..4

Links

Crossrefs

Columns 1-7 are A007581(n-2), A198900, A198901, A198902, A198903, A198904, A198905.
Main diagonal is A198899.
Cf. A207997 (3 colorings), A198715 (4 colorings), A222144 (labeled 5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

A198982 T(n,k) = number of n X k 0..5 arrays with values 0..5 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, 481, 1835, 481, 15, 52, 8731, 146286, 146286, 8731, 52, 202, 174454, 12662226, 53082012, 12662226, 174454, 202, 855, 3603244, 1112962873, 19622872903, 19622872903, 1112962873, 3603244, 855, 3845, 75251971
Offset: 1

Views

Author

R. H. Hardin, Nov 01 2011

Keywords

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 6 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
.....1...........1.................2........................5
.....1...........4................34......................481
.....2..........34..............1835...................146286
.....5.........481............146286.................53082012
....15........8731..........12662226..............19622872903
....52......174454........1112962873............7267830860056
...202.....3603244.......98102456246.........2692353648978984
...855....75251971.....8651794282083.......997397244990907738
..3845..1577395861...763087851014929....369492074075459555844
.18002.33105096904.67305520316532514.136880688981914387733120
...
Some solutions with all values from 0 to 5 for n=6, k=4:
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0
..0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1
..2..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0
..1..2..0..2....4..1..0..1....3..1..0..4....3..4..2..1....3..4..2..5
..4..5..2..1....5..4..2..4....5..2..3..1....1..5..1..5....5..1..5..2

Links

Crossrefs

Columns 1-7 are A056272(n-1), A198976, A198977, A198978, A198979, A198980, A198981.
Main diagonal is A198975.
Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A222281 (labeled 6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

A198723 T(n,k) = number of n X k 0..6 arrays with values 0..6 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, 499, 2027, 499, 15, 52, 10507, 232841, 232841, 10507, 52, 203, 272410, 34003792, 173549032, 34003792, 272410, 203, 876, 7817980, 5315840795, 141168480719, 141168480719, 5315840795, 7817980, 876, 4111
Offset: 1

Views

Author

R. H. Hardin, Oct 29 2011

Keywords

Comments

Number of colorings of the grid graph P_n X P_k using a maximum of 7 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

Examples

			Table starts
.....1............1...................2.......................5
.....1............4..................34.....................499
.....2...........34................2027..................232841
.....5..........499..............232841...............173549032
....15........10507............34003792............141168480719
....52.......272410..........5315840795.........116492275674072
...203......7817980........846047363854.......96356630422085931
...876....234638905.....135284283124811....79732515488691835557
..4111...7176366133...21658679381667910.65980773070548173552412
.20648.221220625936.3468618095206638077
...
Some solutions with all values 0 to 6 for n=3, k=3:
..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..0....0..1..2
..3..2..4....2..3..1....3..4..5....1..3..4....3..4..3....2..3..4....3..4..3
..4..5..6....4..5..6....6..2..4....5..0..6....1..5..6....5..4..6....5..6..2

Links

Crossrefs

Columns 1-7 are A056273(n-1), A198717, A198718, A198719, A198720, A198721, A198722.
Main diagonal is A198716.
Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A222340 (labeled 7 colorings), A198914 (8 colorings), A207868 (unlimited).

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).

A208301 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 antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 1, 2, 2, 5, 5, 5, 42, 52, 15, 15, 602, 2906, 877, 52, 52, 12840, 373780, 433252, 21147, 203, 203, 373780, 87852626, 656404264, 113503692, 678570, 877, 877, 14050312, 33093356640, 2227156082842, 2475181138384, 46538017584, 27644437, 4140
Offset: 1

Views

Author

R. H. Hardin, Feb 25 2012

Keywords

Examples

			Table starts
....1..........1.................2.....................5
....2..........5................42...................602
....5.........52..............2906................373780
...15........877............433252.............656404264
...52......21147.........113503692.........2475181138384
..203.....678570.......46538017584.....17131843186425504
..877...27644437....27700815674032.196551307092757144384
.4140.1382958545.22702140562948192
Some solutions for n=4 k=3
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0
..0..1..0....0..1..0....0..1..0....0..1..0....2..3..0....0..3..0....0..1..0
..0..1..0....0..2..1....0..1..0....0..1..0....0..2..0....0..1..0....2..1..0
..0..2..1....0..2..0....0..1..0....0..1..2....0..1..0....0..3..0....2..1..2

Links

Crossrefs

Columns 1..6 are A000110, A099977(n-1), A208297, A208298, A208299, A208300
Rows 1..7 are A000110(n-1), A208302, A208303, A208305, A208305, A208306, A208307.
Main diagonal is A361450.
Cf. A207868.

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.

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.

A208021 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 5, 7, 7, 5, 15, 87, 270, 87, 15, 52, 1657, 27093, 27093, 1657, 52, 203, 43833, 5252041, 30066912, 5252041, 43833, 203, 877, 1515903, 1688298227, 80318704605, 80318704605, 1688298227, 1515903, 877, 4140, 65766991
Offset: 1

Views

Author

R. H. Hardin, Feb 22 2012

Keywords

Comments

Equivalently, the number of colorings of the n x k king graph using any number of colors up to permutation of the colors. - Andrew Howroyd, Jun 25 2017

Examples

			Table starts
...1........1............2...............5...............15..............52
...1........1............7..............87.............1657...........43833
...2........7..........270...........27093..........5252041......1688298227
...5.......87........27093........30066912......80318704605.421673189900658
..15.....1657......5252041.....80318704605.3662498214110836
..52....43833...1688298227.421673189900658
.203..1515903.819147302097
.877.65766991
...
Some solutions for n=4 k=3
..0..1..2....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..2
..2..3..4....2..3..2....2..3..2....2..3..2....2..3..2....2..3..2....2..3..0
..5..6..0....4..0..4....0..1..0....4..1..0....0..1..0....0..4..0....4..5..4
..2..3..1....1..2..1....2..3..4....5..2..3....2..4..2....1..2..1....0..1..2

Links

Crossrefs

Columns 1-5 are A000110(n-1), A020556(n-1), A208018, A208019, A208020.
Main diagonal is A289136.
Cf. A207868, A212208, A212209.
Showing 1-10 of 18 results. Next

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