A208096 -id:A208096 - 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.

A208093 Number of nX3 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

2, 30, 1573, 192328, 43366459, 15769674462, 8494585220016, 6391850672195207, 6435536606760976374, 8388789053759733374255, 13792349692923790472807338, 28002764873470436036725295426, 68986219453948522377865096287773

Offset: 1

R. H. Hardin Feb 23 2012

nonn

Column 3 of A208096

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

R. H. Hardin, Table of n, a(n) for n = 1..16

A208094 Number of n X 4 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, 5, 377, 169064, 235862938, 746823293346, 4493602584256529, 45881957995776221396, 734971289403287420883126, 17434398033181126785548889533, 585880828202059360820577364423099, 26929433656271781956071918468836389588, 1645382407173932261418519657416983542506695

Offset: 0

R. H. Hardin, Feb 23 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..2....0..1..0..1....0..1..2..1....0..1..0..1....0..1..0..2
..2..1..0..1....2..1..0..2....0..1..0..1....0..2..0..1....2..1..0..1
..0..1..2..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..2

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

Column 4 of A208096.

a(0)=1 prepended and terms a(8) and beyond from Andrew Howroyd, May 17 2020

A208095 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 15, 7239, 34438557, 677352910013, 37155328943771767, 4558466722941178786343, 1086389216314310418981064791, 455984828225593734632397603864943, 313575182393219205765164919469780819082, 334231574923251058616578365205688685770273545

Offset: 0

R. H. Hardin, Feb 23 2012

nonn

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

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

Column 5 of A208096.

a(0)=1 prepended and terms a(6) and beyond from Andrew Howroyd, May 17 2020

A208097 Number of 2 X n 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

2, 4, 30, 377, 7239, 193228, 6752442, 296290708, 15835464207, 1007305486325, 74890158775564, 6413015600048526, 624933541074620780, 68603269124243415049, 8411144435499643711885, 1143251056778815843116186

Offset: 1

R. H. Hardin, Feb 23 2012

nonn

Row 2 of A208096.

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A208098 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 5, 34, 1573, 169064, 34438557, 11535531783, 5804338800147, 4121852595871393, 3947133396896179889, 4923290609971869799119, 7783034938833777039389506, 15253558021465456746321690675, 36391805974300638618769192592189, 104086634920105554145003030677202100

Offset: 0

R. H. Hardin, Feb 23 2012

nonn

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

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

Row 3 of A208096.

a(0)=1 prepended and terms a(9) and beyond from Andrew Howroyd, May 17 2020

A208099 Number of 4 X n 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, 15, 500, 192328, 235862938, 677352910013, 3773408294000427, 36179066767453804155, 549736601190850705047301, 12463226118187748082979153202, 402612019211536786633308878052340, 17870804510325656079748707416649732732, 1058340866272922899343613575761029687845720

Offset: 0

R. H. Hardin, Feb 23 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..2....0..1..0..1....2..1..0..1....2..1..0..1
..0..1..2..1....2..1..0..1....2..1..0..2....0..3..0..1....0..1..2..1
..0..1..3..1....0..1..0..2....0..1..0..1....4..1..0..1....0..1..0..1

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

Row 4 of A208096.

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

A208100 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 52, 10900, 43366459, 746823293346, 37155328943771767, 4226534204353128532380, 947741983969338430602294081, 378161752496622695975714927056844, 249107761813131722624691729833262083766, 255811781476365074058962776043470702114960079

Offset: 0

R. H. Hardin, Feb 23 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..2..1....0..2..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..1..0..3
..0..1..0..1....0..2..0..1....0..1..0..1....0..1..2..1....0..1..0..1
..3..1..0..1....0..1..3..1....0..1..0..1....0..1..0..1....0..3..0..1

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

Row 5 of A208096.

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

A361449 Number of colorings of an n X n grid up to permutation of the colors with no element having the same color as any horizontal, diagonal or antidiagonal neighbor.

Original entry on oeis.org

1, 4, 1573, 235862938, 37155328943771767, 12458003910177278332403197817, 15868284521418341362691384074620547198698934, 126024243590219798408446284849897811759970155660106999854057796, 9633603531065043175094488158875624821526224424118142906010095879389674957042528276201

Offset: 1

Andrew Howroyd, Mar 13 2023

nonn

Main diagonal of A208096.

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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A208093 Number of nX3 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).

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A208094 Number of n X 4 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).

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A208095 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

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A208097 Number of 2 X n 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).

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A208098 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

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A208099 Number of 4 X n 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).

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Extensions

A208100 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, diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).

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Examples

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Crossrefs

Extensions

A361449 Number of colorings of an n X n grid up to permutation of the colors with no element having the same color as any horizontal, diagonal or antidiagonal neighbor.

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