A208353 -id:A208353 - cp's OEIS frontend

A208001 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 knight-move neighbor (colorings ignoring permutations of colors).

1, 2, 2, 5, 15, 5, 15, 114, 114, 15, 52, 1657, 4141, 1657, 52, 203, 36401, 426422, 426422, 36401, 203, 877, 1094076, 86545486, 450288795, 86545486, 1094076, 877, 4140, 42436913, 29169661126, 1182700979380, 1182700979380, 29169661126, 42436913, 4140

Offset: 1

R. H. Hardin, Feb 22 2012

			Table starts
....1........2...........5............15............52.........203
....2.......15.........114..........1657.........36401.....1094076
....5......114........4141........426422......86545486.29169661126
...15.....1657......426422.....450288795.1182700979380
...52....36401....86545486.1182700979380
..203..1094076.29169661126
..877.42436913
.4140
...
Some solutions for n=4 k=3
..0..0..0....0..0..0....0..0..0....0..1..0....0..0..1....0..0..0....0..0..0
..1..0..1....1..2..1....1..0..1....1..0..1....0..0..1....1..0..1....1..0..1
..2..1..2....2..1..2....2..1..2....0..1..2....2..2..1....2..1..2....2..2..2
..1..0..3....3..0..0....1..0..1....1..2..1....2..3..1....1..2..1....1..0..1

Andrew Howroyd, Table of n, a(n) for n = 1..66 (terms 1..39 from R. H. Hardin).
Eric Weisstein's World of Mathematics, Knight Graph.
Eric Weisstein's World of Mathematics, Vertex Coloring.

Columns 1..4 are A000110, A207998, A207999, A208000.
Main diagonal is A361453.
Cf. A208434 (3 colorings), A208353 (4 colorings).
Cf. A207868 (grid graph).

A208347 Number of nX2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

2, 15, 100, 868, 7780, 69988, 629860, 5668708, 51018340, 459165028, 4132485220, 37192366948, 334731302500, 3012581722468, 27113235502180, 244019119519588, 2196172075676260, 19765548681086308, 177889938129776740

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 2 of A208353

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 10*a(n-1) -9*a(n-2) for n>4

A208348 Number of nX3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

5, 100, 1095, 12625, 153237, 1901508, 23658861, 294608660, 3672171940, 45806539501, 571496743787, 7130666296577, 88976864630029, 1110304369879641, 13855224093424061, 172897096309149243, 2157565319312754303

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 3 of A208353

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 21*a(n-1) -90*a(n-2) -532*a(n-3) +5973*a(n-4) -31315*a(n-5) +73172*a(n-6) +692866*a(n-7) -5872588*a(n-8) +14338130*a(n-9) +13545534*a(n-10) -238643374*a(n-11) +1047870400*a(n-12) -1941550084*a(n-13) -2024947104*a(n-14) +17313536656*a(n-15) -33786142200*a(n-16) +21548688152*a(n-17) +32421829160*a(n-18) -107335908376*a(n-19) +165792590624*a(n-20) -118619608528*a(n-21) -73538891712*a(n-22) +207386497216*a(n-23) -223952516832*a(n-24) +322902169696*a(n-25) -245567709568*a(n-26) -217360125376*a(n-27) +464272398720*a(n-28) -172433924352*a(n-29) -145159584768*a(n-30) +86842756096*a(n-31) +128366311424*a(n-32) -108640727040*a(n-33) -53571584000*a(n-34) +74317824000*a(n-35) -18063360000*a(n-36) for n>39

A208349 Number of n X 4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

15, 868, 12625, 230387, 4773885, 103672036, 2280287753, 50481169071, 1122098238432, 24983185355723, 556622494082921, 12405478452873059, 276529980588607690, 6164555722628477878, 137428302821781111484

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 4 of A208353.

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

R. H. Hardin, Table of n, a(n) for n = 1..129

Cf. A208353.

A208350 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

51, 7780, 153237, 4773885, 191586797, 8045978096, 340596199800, 14513602070899, 621231491393354, 26619820042892506, 1141266433540198765, 48945495491297801080, 2099487944721769270814, 90063058254133100176716

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 5 of A208353

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

R. H. Hardin, Table of n, a(n) for n = 1..29

A208346 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

1, 15, 1095, 230387, 191586797, 647640659639

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Diagonal of A208353

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

A208351 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

187, 69988, 1901508, 103672036, 8045978096, 647640659639, 52428246114853

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 6 of A208353

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

A208352 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

Original entry on oeis.org

715, 629860, 23658861, 2280287753, 340596199800, 52428246114853

Offset: 1

R. H. Hardin Feb 25 2012

nonn

Column 7 of A208353

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

cp's OEIS Frontend

A208001 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 knight-move neighbor (colorings ignoring permutations of colors).

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A208347 Number of nX2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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A208348 Number of nX3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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A208349 Number of n X 4 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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A208350 Number of nX5 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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A208346 Number of n X n 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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A208351 Number of nX6 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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A208352 Number of nX7 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).

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