A216460 -id:A216460 - cp's OEIS frontend

A216612 T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nXk array with new integer colors introduced in row major order.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 5, 2, 2, 5, 15, 20, 15, 5, 2, 15, 41, 203, 67, 52, 5, 5, 52, 716, 3429, 4140, 1335, 203, 15, 5, 203, 2847, 83440, 83437, 115975, 6097, 877, 15, 15, 877, 83440, 2711768, 18171918, 20880505, 4213597, 192713, 4140, 52, 15, 4140

Offset: 1

R. H. Hardin Sep 10 2012

Table starts
...1......1.........1............1..............1................2
...1......1.........1............2..............5...............15
...1......2.........2...........15.............41..............716
...2......5........20..........203...........3429............83440
...2.....15........67.........4140..........83437.........18171918
...5.....52......1335.......115975.......20880505.......6423127757
...5....203......6097......4213597......942420901....3376465219485
..15....877....192713....190899322...484968748793.2486327138729353
..15...4140...1094076..10480142147.33862631596393
..52..21147..49055292.682076806159
..52.115975.329588907
.203.678570

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

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)
Row 4 is A216462
Row 6 is A216464
Even squares: A216460

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.

A216462 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 4Xn array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 5, 20, 203, 3429, 83440, 2711768, 112073062, 5691327040, 346212384169, 24737419691764, 2043836452962923, 192779435018929754, 20538493062072286871, 2449347793873500266618, 324446721789278481458200

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Row 4 of A216460

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

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

A216457 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX3 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 7, 20, 322, 1335, 36401, 192713, 7712455, 49055292, 2659544320, 19602119017, 1367160898137, 11399696350555, 986429423363481, 9146845346099410, 955922762706415420, 9731199828137067515, 1203020866861467699281

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Column 3 of A216460

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

R. H. Hardin, Table of n, a(n) for n = 1..95

A216458 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX5 array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 5, 203, 3429, 580479, 20880505, 8195008751, 484968748793, 348950573407587, 30012936243058237, 34789578208577116867, 4040674235335081456861, 6947043903258606579346103, 1037627124289198371293601937

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Column 5 of A216460

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

R. H. Hardin, Table of n, a(n) for n = 1..24

A216461 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 3Xn array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 2, 7, 15, 203, 716, 17733, 83440, 3137543, 18171918, 942426468, 6423127757, 433245459699, 3376465219485, 284615058572536, 2486327138729353, 254421641605158901, 2454996141671330713, 298288744434946125073

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Row 3 of A216460

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

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

A216464 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 6Xn array with new integer colors introduced in row major order.

Original entry on oeis.org

5, 52, 1335, 115975, 20880505, 6423127757, 3030359756694, 2043836470040286

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Row 6 of A216460

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

A216456 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an n X n array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 7, 203, 580479, 6423127757, 22530453266592757

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Diagonal of A216460

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

A216459 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX7 array with new integer colors introduced in row major order.

Original entry on oeis.org

5, 52, 17733, 2711768, 6423148007, 3030359756694, 22530453266592757, 22413340656366875404, 380159173982235374080849, 663445132155786673512833428, 21523865504501144083392978709171

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Column 7 of A216460

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

A216463 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 5Xn array with new integer colors introduced in row major order.

Original entry on oeis.org

5, 15, 322, 4140, 580479, 18171918, 6423148007, 346212390266, 232431640956990, 18633407258171930, 20538497277155387947

Offset: 1

R. H. Hardin Sep 07 2012

nonn

Row 5 of A216460

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

cp's OEIS Frontend

A216612 T(n,k)=Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd 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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A216462 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 4Xn array with new integer colors introduced in row major order.

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A216457 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX3 array with new integer colors introduced in row major order.

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A216458 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX5 array with new integer colors introduced in row major order.

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A216461 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 3Xn array with new integer colors introduced in row major order.

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A216464 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 6Xn array with new integer colors introduced in row major order.

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A216456 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an n X n array with new integer colors introduced in row major order.

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A216459 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX7 array with new integer colors introduced in row major order.

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A216463 Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of a 5Xn array with new integer colors introduced in row major order.

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Examples