A216031 -id:A216031 - cp's OEIS frontend

A215959 T(n,k)=Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 4, 10, 4, 2, 2, 12, 29, 29, 12, 2, 5, 34, 366, 313, 366, 34, 5, 5, 136, 1534, 6150, 6150, 1534, 136, 5, 15, 500, 35167, 145563, 847594, 145563, 35167, 500, 15, 15, 2440, 188835, 5219070, 30312074, 30312074, 5219070, 188835, 2440, 15

Offset: 1

R. H. Hardin Aug 28 2012

Table starts
..1.....1........1...........1............2.............2.............5
..1.....1........2...........4...........12............34...........136
..1.....2.......10..........29..........366..........1534.........35167
..1.....4.......29.........313.........6150........145563.......5219070
..2....12......366........6150.......847594......30312074...10289785215
..2....34.....1534......145563.....30312074....9260821180.4761748786964
..5...136....35167.....5219070..10289785215.4761748786964
..5...500...188835...208181894.609400419815
.15..2440..6618472.11412814314
.15.10900.42756208

			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..1..x..0....x..2..x..3....x..2..x..3
..1..x..4..x....4..x..3..x....2..x..0..x....4..x..5..x....4..x..5..x
..x..0..x..5....x..5..x..2....x..3..x..1....x..5..x..2....x..0..x..4

R. H. Hardin, Table of n, a(n) for n = 1..84

Column 1 is A000110(floor((n-1)/2))

Odd squares: A216031

A216025 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX2 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 2, 2, 5, 12, 42, 136, 602, 2440, 12840, 61912, 373780, 2075312, 14050312, 87852160, 656404264, 4548247264, 37060650272, 281121815712, 2475181138384, 20358402201792, 192262536609952, 1701534399324544, 17131843186425504

Offset: 1

R. H. Hardin Aug 30 2012

nonn

Column 2 of A216031

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

R. H. Hardin, Table of n, a(n) for n = 1..123

A216026 Number of horizontal, vertical and diagonal 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, 2, 4, 29, 97, 1534, 7050, 188835, 1084180, 42756208, 291120551, 15590248868, 121920095674, 8414029179365, 73953763887277, 6340176007793060, 61657373569634586, 6390402969619162909, 67948766672072844798

Offset: 1

R. H. Hardin Aug 30 2012

nonn

Column 3 of A216031

			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..2..x....x..3..x....x..3..x....x..2..x....x..2..x....x..2..x....x..3..x
..0..x..1....0..x..4....4..x..5....3..x..0....2..x..1....3..x..4....3..x..0

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

A216027 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX4 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 5, 29, 371, 6150, 167130, 5219070, 233834847, 11412814314, 741757937068, 51088102234508, 4468693984145541, 407520605922011467, 45668525708806007925, 5279748839226156263229, 732043230152926700952839

Offset: 1

R. H. Hardin Aug 30 2012

nonn

Column 4 of A216031

			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....2..x..1..x....0..x..2..x....0..x..1..x....2..x..1..x
..x..2..x..3....x..3..x..2....x..1..x..0....x..1..x..2....x..1..x..3
..3..x..4..x....1..x..4..x....3..x..4..x....1..x..3..x....1..x..3..x

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

A216024 Number of horizontal, vertical and diagonal 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, 2, 4, 371, 146327, 10311562327

Offset: 1

R. H. Hardin, Aug 30 2012

nonn

Diagonal of A216031.

			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....0..x..2..x....2..x..3..x....2..x..3..x....2..x..3..x
..x..3..x..4....x..1..x..0....x..3..x..0....x..4..x..2....x..1..x..4
..3..x..0..x....3..x..0..x....4..x..2..x....5..x..2..x....1..x..0..x

Cf. A216031.

A216028 Number of horizontal, vertical and diagonal 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, 12, 97, 6150, 146327, 30312074, 1355988481, 609400419815, 42505520884540, 33926900616984192, 3335043669700991645

Offset: 1

R. H. Hardin Aug 30 2012

nonn

Column 5 of A216031

			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
..1..x..2..x..3....0..x..2..x..3....2..x..3..x..4....0..x..2..x..0
..x..4..x..0..x....x..4..x..0..x....x..5..x..4..x....x..2..x..0..x
..4..x..1..x..2....4..x..5..x..1....0..x..4..x..0....3..x..4..x..5

A216029 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX6 array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 42, 1534, 167130, 30312074, 10311562327, 4761748786964, 3439948243132701

Offset: 1

R. H. Hardin Aug 30 2012

nonn

Column 6 of A216031

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

A216030 Number of horizontal, vertical and diagonal 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, 136, 7050, 5219070, 1355988481, 4761748786964

Offset: 1

R. H. Hardin Aug 30 2012

nonn

Column 7 of A216031

			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
..0..x..1..x..3..x..4....0..x..1..x..3..x..4....0..x..1..x..0..x..3
..x..2..x..5..x..4..x....x..2..x..0..x..5..x....x..2..x..4..x..5..x
..2..x..3..x..0..x..3....2..x..3..x..6..x..0....6..x..5..x..7..x..1

cp's OEIS Frontend

A215959 T(n,k)=Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nXk array with new integer colors introduced in row major order.

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A216025 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX2 array with new integer colors introduced in row major order.

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A216026 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX3 array with new integer colors introduced in row major order.

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A216027 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX4 array with new integer colors introduced in row major order.

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A216024 Number of horizontal, vertical and diagonal 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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A216028 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX5 array with new integer colors introduced in row major order.

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A216029 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX6 array with new integer colors introduced in row major order.

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Examples

A216030 Number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an nX7 array with new integer colors introduced in row major order.

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