A216612 -id:A216612 - cp's OEIS frontend

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.

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

R. H. Hardin Sep 07 2012

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

			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

R. H. Hardin, Table of n, a(n) for n = 1..96

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

A208051 Number of n X 3 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

2, 15, 716, 83440, 18171918, 6423127757, 3376465219485, 2486327138729353, 2454996141671330713, 3143641561804718358884, 5084413934903476204054959, 10166624612435356414640715276, 24691194409056203926713355839051

Offset: 1

R. H. Hardin, Feb 22 2012

nonn

			Some solutions for n=4
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..2..3..1....2..3..1....2..3..2....2..3..1....2..3..2....2..3..4....2..3..1
..0..2..0....0..4..5....0..4..0....1..0..2....0..1..4....0..5..0....4..5..3
..1..3..1....5..3..4....1..2..1....2..3..0....2..0..1....1..2..1....0..6..4

Andrew Howroyd, Table of n, a(n) for n = 1..100 (first 20 terms from R. H. Hardin)

Column 3 of A208054.

Column 6 of A216460 and column 6 of A216612.

A216609 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX3 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 2, 20, 67, 1335, 6097, 192713, 1094076, 49055292, 329588907, 19602119017, 151146594991, 11399696350555, 98774751736976, 9146845346099410, 87700687826082507, 9731199828137067515, 102042888281439150263

Offset: 1

R. H. Hardin Sep 10 2012

nonn

Column 3 of A216612

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

R. H. Hardin, Table of n, a(n) for n = 1..97

A216610 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX5 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 5, 41, 3429, 83437, 20880505, 942420901, 484968748793, 33862631596393, 30012936243058237, 2941251571063448753, 4040674235335081456861, 522798156103780731219765, 1037627124289198371293601937

Offset: 1

R. H. Hardin Sep 10 2012

nonn

Column 5 of A216612

			Some solutions for n=4
..x..0..x..1..x....x..0..x..1..x....x..0..x..1..x....x..0..x..1..x
..2..x..3..x..4....2..x..3..x..0....2..x..3..x..4....1..x..2..x..3
..x..5..x..0..x....x..4..x..1..x....x..5..x..6..x....x..4..x..1..x
..2..x..1..x..5....3..x..0..x..2....4..x..1..x..5....5..x..6..x..2

R. H. Hardin, Table of n, a(n) for n = 1..25

A216613 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of a 3 X n array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 2, 2, 15, 41, 716, 2847, 83440, 426422, 18171918, 112072316, 6423127757, 46054057965, 3376465219485, 27457462735926, 2486327138729353, 22530435476364494, 2454996141671330713, 24463971326544703312

Offset: 1

R. H. Hardin, Sep 10 2012

nonn

Row 3 of A216612.

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

R. H. Hardin, Table of n, a(n) for n = 1..41

Cf. A216612.

A216608 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an n X n array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 2, 203, 83437, 6423127757, 2043835395791757, 324446722340564335642246

Offset: 1

R. H. Hardin Sep 10 2012

nonn

Diagonal of A216612

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

A216611 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX7 array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 52, 2847, 2711768, 732209051, 3030359756694, 2043835395791757, 22413340656366875404, 28985266574404467248885, 663445132155786673512833428, 1425339594540323247000177579385

Offset: 1

R. H. Hardin Sep 10 2012

nonn

Column 7 of A216612

			Some solutions for n=4
..x..0..x..1..x..2..x....x..0..x..1..x..2..x....x..0..x..1..x..2..x
..1..x..2..x..3..x..4....1..x..2..x..3..x..1....1..x..2..x..3..x..4
..x..4..x..5..x..2..x....x..0..x..4..x..2..x....x..5..x..6..x..5..x
..0..x..6..x..4..x..3....5..x..2..x..5..x..0....0..x..2..x..1..x..7

A216614 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of a 5Xn array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 15, 67, 4140, 83437, 18171918, 732209051, 346212390266, 22294303538804, 18633407258171930, 1714659308610029464

Offset: 1

R. H. Hardin Sep 10 2012

nonn

Row 5 of A216612

			Some solutions for n=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....2..x..3..x....2..x..3..x....2..x..3..x
..x..1..x..2....x..4..x..1....x..0..x..4....x..4..x..2....x..1..x..4
..0..x..3..x....0..x..5..x....5..x..3..x....3..x..1..x....4..x..0..x
..x..1..x..0....x..3..x..4....x..6..x..4....x..2..x..3....x..3..x..2

A216615 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of a 7Xn array with new integer colors introduced in row major order.

Original entry on oeis.org

5, 203, 6097, 4213597, 942420901, 3376465219485, 2043835395791757, 20538493137072741201

Offset: 1

R. H. Hardin Sep 10 2012

nonn

Row 7 of A216612

			Some solutions for n=4
..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
..1..x..2..x....1..x..2..x....1..x..2..x....1..x..2..x....1..x..2..x
..x..0..x..1....x..0..x..3....x..0..x..3....x..0..x..3....x..0..x..3
..1..x..3..x....2..x..4..x....3..x..4..x....3..x..2..x....4..x..1..x
..x..4..x..5....x..0..x..5....x..5..x..1....x..4..x..5....x..5..x..2
..0..x..3..x....5..x..6..x....1..x..6..x....3..x..6..x....0..x..4..x
..x..4..x..6....x..7..x..5....x..0..x..4....x..2..x..0....x..1..x..3

cp's OEIS Frontend

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.

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A208051 Number of n X 3 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).

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A216609 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX3 array with new integer colors introduced in row major order.

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A216610 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX5 array with new integer colors introduced in row major order.

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A216613 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of a 3 X n array with new integer colors introduced in row major order.

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A216608 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an n X n array with new integer colors introduced in row major order.

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A216611 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX7 array with new integer colors introduced in row major order.

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Examples

A216614 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of a 5Xn array with new integer colors introduced in row major order.

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Author

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Comments

Examples

A216615 Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of a 7Xn array with new integer colors introduced in row major order.

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