A208301 -id:A208301 - cp's OEIS frontend

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).

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

R. H. Hardin, Feb 21 2012

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

			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

Andrew Howroyd, Table of n, a(n) for n = 1..231 (terms 1..49 from R. H. Hardin)
Eric Weisstein's World of Mathematics, Grid Graph.
Eric Weisstein's World of Mathematics, Vertex Coloring.
Wikipedia, Graph Coloring.

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.

A208302 Number of 2Xn 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

2, 5, 42, 602, 12840, 373780, 14050312, 656404264, 37060650272, 2475181138384, 192262536609952, 17131843186425504, 1731360533569170048, 196551307092757144384, 24860319276726031245440, 3478554309451804194287232

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Row 2 of A208301

			Some solutions for n=4
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..2..3..4..2....2..1..2..0....2..1..0..3....0..1..0..1....0..1..0..2

R. H. Hardin, Table of n, a(n) for n = 1..21

A208297 Number of nX3 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

2, 42, 2906, 433252, 113503692, 46538017584, 27700815674032, 22702140562948192, 24626774613248937584, 34296243004533645925408, 59839415643338575851475744, 128222446504879248765189962560, 331858429902640216546970620625280

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 3 of A208301

			Some solutions for n=4
..0..1..0....0..1..0....0..1..2....0..1..0....0..1..0....0..1..2....0..1..2
..0..1..0....0..1..0....0..1..2....0..1..0....2..3..0....0..3..1....0..3..0
..0..1..0....2..1..2....0..1..0....0..1..0....0..2..0....0..2..0....0..1..0
..0..2..1....0..1..0....0..1..0....0..1..0....0..1..0....3..1..0....0..3..0

R. H. Hardin, Table of n, a(n) for n = 1..49

A208298 Number of nX4 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

5, 602, 373780, 656404264, 2475181138384, 17131843186425504, 196551307092757144384, 3478554309451804194287232, 90015726535715347904300537088, 3267494997828691666636390741293568

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 4 of A208301

			Some solutions for n=4
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..0..1..0..1....0..1..0..2....0..1..0..1....0..1..0..1....2..1..0..1
..2..1..0..2....2..1..0..1....2..1..0..1....0..1..0..1....0..2..0..1
..0..1..0..1....0..1..0..2....0..1..0..1....2..3..0..1....0..1..0..1

R. H. Hardin, Table of n, a(n) for n = 1..20

A208299 Number of n X 5 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, 15, 12840, 87852626, 2227156082842, 148049849095504726, 21183598567292002167082, 5737167377815628378510929822, 2685975192008614716088213333413834, 2031667423243870021802621888823332638846, 2356075680798443401764258655433216618467066594

Offset: 0

R. H. Hardin, Feb 25 2012

nonn

			Some solutions for n=4:
..0..1..0..1..0....0..1..0..1..0....0..1..2..0..3....0..1..0..1..0
..2..1..0..1..2....2..1..0..1..0....0..1..2..4..0....0..1..0..1..0
..0..1..0..1..0....0..1..0..2..0....0..1..0..1..0....0..1..0..1..0
..0..1..0..1..0....0..1..0..2..0....0..1..0..1..4....0..1..2..1..0

Andrew Howroyd, Table of n, a(n) for n = 0..100

Column 5 of A208301.

a(0)=1 prepended and terms a(10) and beyond from Andrew Howroyd, May 18 2020

A208300 Number of n X 6 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, 52, 373780, 33093356640, 14216420563705724, 19558496206477343793824, 67939294184937980415465539016, 510275358863420934339418249390485008, 7427072102775408021555037479377677353344288, 193059270325130351714478780835691676245238854091968

Offset: 0

R. H. Hardin, Feb 25 2012

nonn

			Some solutions for n=4:
..0..1..0..1..0..1....0..1..0..1..2..1....0..1..0..1..0..1....0..1..0..1..2..1
..0..1..0..1..0..1....0..1..0..1..0..1....0..1..0..1..0..1....0..1..0..3..0..1
..2..1..3..1..0..1....2..1..2..1..0..1....0..1..0..1..0..1....0..1..0..2..3..0
..0..1..0..1..2..0....2..0..2..3..0..1....0..1..0..1..0..1....0..1..0..1..2..0

Andrew Howroyd, Table of n, a(n) for n = 0..50

Column 6 of A208301.

a(0)=1 prepended and terms a(6) and beyond from Andrew Howroyd, May 18 2020

A208303 Number of 3 X n 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, 5, 52, 2906, 373780, 87852626, 33093356640, 18383354934430, 14216420560211868, 14670987603972303070, 19558496205580909812744, 32828323774419481541135978, 67939294184199439807451132308, 170381709310740181061939305134514, 510275358861788633812686061715278224

Offset: 0

R. H. Hardin, Feb 25 2012

nonn

			Some solutions for n=4:
..0..1..2..0....0..1..0..1....0..1..0..2....0..1..0..1....0..1..2..0
..2..1..2..0....0..1..0..1....3..1..0..2....0..1..0..1....3..0..1..0
..0..3..1..0....0..1..2..1....0..1..0..1....2..1..2..0....1..0..3..0

Andrew Howroyd, Table of n, a(n) for n = 0..100

Row 3 of A208301.

a(0)=1 prepended and terms a(10) and beyond from Andrew Howroyd, May 18 2020

A208305 Number of 5 X n 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, 52, 21147, 113503692, 2475181138384, 148049849095504726, 19558496206477343793824, 4971673449365938875551493054, 2209363673053161750976745846408452, 1599235210372714053663919266990430641290, 1785670329039896818784300269276903576597674264

Offset: 0

R. H. Hardin, Feb 25 2012

nonn

			Some solutions for n=4:
..0..1..0..1....0..1..0..1....0..1..2..0....0..1..0..1....0..1..0..1
..0..1..0..1....0..1..0..1....3..0..1..0....0..1..0..1....0..2..0..1
..0..1..2..0....0..1..0..1....4..0..1..0....0..1..0..1....0..1..0..1
..0..1..2..0....0..1..2..0....1..2..1..0....0..2..0..1....0..2..0..1
..0..1..2..3....0..1..2..0....0..2..1..4....0..1..0..1....0..1..2..0

Andrew Howroyd, Table of n, a(n) for n = 0..100

Row 5 of A208301.

a(0)=1 prepended and terms a(7) and beyond from Andrew Howroyd, May 18 2020

A208306 Number of 6 X n 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, 203, 678570, 46538017584, 17131843186425504, 21183598567292002167082, 67939294184937980415465539016, 479196921365748673300774676923278618, 6626004995909411145707148239379062019989108, 164986885310084515129040822858386474548745376110410

Offset: 0

R. H. Hardin, Feb 25 2012

nonn

			Some solutions for n=4:
..0..1..2..0....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..0..1..2..0....0..1..0..1....2..1..0..1....0..1..0..1....2..1..0..1
..0..1..2..0....0..1..0..1....0..1..0..1....2..1..0..1....0..3..0..3
..0..1..2..0....2..1..3..0....2..1..2..0....0..1..2..0....0..1..0..1
..0..1..2..0....0..1..2..0....0..1..2..0....0..1..2..0....3..1..0..1
..0..1..2..3....0..1..2..0....0..3..1..0....0..1..2..0....0..1..0..1

Andrew Howroyd, Table of n, a(n) for n = 0..50

Row 6 of A208301.

a(0)=1 prepended and terms a(6) and beyond from Andrew Howroyd, May 18 2020

A208307 Number of 7 X n 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, 877, 27644437, 27700815674032, 196551307092757144384, 5737167377815628378510929822, 510275358863420934339418249390485008, 114130286115375064054502412158789812265958284, 56140177561453730943968268473396800731088097525712216

Offset: 0

R. H. Hardin Feb 25 2012

nonn

			Some solutions for n=4:
..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1
..0..1..0..1....0..1..0..1....0..1..2..0....0..1..0..1....0..1..0..1
..0..1..0..1....0..1..0..1....0..1..2..0....0..1..0..1....0..1..0..1
..2..1..0..1....0..1..0..1....0..1..2..0....0..1..0..1....0..1..0..1
..0..1..2..0....0..1..0..1....0..1..2..0....0..1..0..1....0..1..0..1
..0..1..2..1....2..1..0..1....0..1..2..0....0..1..0..1....0..2..0..1
..0..1..0..1....0..1..0..1....0..1..2..0....0..1..0..1....0..1..0..1

Andrew Howroyd, Table of n, a(n) for n = 0..50

Row 7 of A208301.

a(0)=1 prepended and terms a(6) and beyond from Andrew Howroyd, May 18 2020

cp's OEIS Frontend

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).

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A208302 Number of 2Xn 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).

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A208297 Number of nX3 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).

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A208298 Number of nX4 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).

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A208299 Number of n X 5 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).

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A208300 Number of n X 6 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).

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A208303 Number of 3 X n 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).

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A208305 Number of 5 X n 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).

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A208306 Number of 6 X n 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).

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Examples

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Crossrefs

Extensions

A208307 Number of 7 X n 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).

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Examples

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