A215959 -id:A215959 - cp's OEIS frontend

A216031 T(n,k) is the number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an n X k array with new integer colors introduced in row major order.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 5, 4, 5, 1, 2, 12, 29, 29, 12, 2, 2, 42, 97, 371, 97, 42, 2, 5, 136, 1534, 6150, 6150, 1534, 136, 5, 5, 602, 7050, 167130, 146327, 167130, 7050, 602, 5, 15, 2440, 188835, 5219070, 30312074, 30312074, 5219070, 188835, 2440, 15, 15, 12840

Offset: 1

R. H. Hardin, Aug 30 2012

			Table starts:
..1.....1........1...........1............1.............2.............2
..1.....2........2...........5...........12............42...........136
..1.....2........4..........29...........97..........1534..........7050
..1.....5.......29.........371.........6150........167130.......5219070
..1....12.......97........6150.......146327......30312074....1355988481
..2....42.....1534......167130.....30312074...10311562327.4761748786964
..2...136.....7050.....5219070...1355988481.4761748786964
..5...602...188835...233834847.609400419815
..5..2440..1084180.11412814314
.15.12840.42756208
.15.61912
.52
Some solutions for n=4 and k=4:
..x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1....x..0..x..1
..2..x..1..x....2..x..3..x....0..x..2..x....0..x..1..x....0..x..1..x
..x..1..x..2....x..1..x..4....x..3..x..0....x..2..x..0....x..1..x..0
..0..x..2..x....3..x..2..x....4..x..0..x....3..x..4..x....1..x..2..x

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

Column 1 is A000110(floor((n-2)/2)) for n>1.

Even squares: A215959.

A215953 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an n X 2 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 1, 2, 4, 12, 34, 136, 500, 2440, 10900, 61912, 322768, 2075312, 12297768, 87852160, 580849872, 4548247264, 33093252880, 281121815712, 2227152575552, 20358402201792, 174131286983712, 1701534399324544, 15604440074084672

Offset: 1

R. H. Hardin, Aug 28 2012

nonn

Column 2 of A215959.

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

R. H. Hardin, Table of n, a(n) for n = 1..122

A215954 Number of horizontal, vertical and diagonal 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, 2, 10, 29, 366, 1534, 35167, 188835, 6618472, 42756208, 2081922515, 15590248868, 993343650912, 8414029179365, 673316834487162, 6340176007793060, 618445940056365121, 6390402969619162909, 742701928727400476918

Offset: 1

R. H. Hardin Aug 28 2012

nonn

Column 3 of A215959

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

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

A215955 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an n X 4 array with new integer colors introduced in row major order.

Original entry on oeis.org

1, 4, 29, 313, 6150, 145563, 5219070, 208181894, 11412814314, 670592486703, 51088102234508, 4085932956830052, 407520605922011467, 42123055901071684382, 5279748839226156263229, 679936583636831702045901

Offset: 1

R. H. Hardin, Aug 28 2012

nonn

Column 4 of A215959.

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

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

Cf. A215959.

A215956 Number of horizontal, vertical and diagonal 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, 12, 366, 6150, 847594, 30312074, 10289785215, 609400419815, 392670408857828, 33926900616984192, 35986649547821568686

Offset: 1

R. H. Hardin Aug 28 2012

nonn

Column 5 of A215959

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

A215957 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nX6 array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 34, 1534, 145563, 30312074, 9260821180, 4761748786964, 3146896493234825

Offset: 1

R. H. Hardin Aug 28 2012

nonn

Column 6 of A215959

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

A215958 Number of horizontal, vertical and diagonal 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, 136, 35167, 5219070, 10289785215, 4761748786964

Offset: 1

R. H. Hardin Aug 28 2012

nonn

Column 7 of A215959

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

cp's OEIS Frontend

A216031 T(n,k) is the number of horizontal, vertical and diagonal neighbor colorings of the odd squares of an n X k array with new integer colors introduced in row major order.

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A215953 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an n X 2 array with new integer colors introduced in row major order.

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A215954 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nX3 array with new integer colors introduced in row major order.

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A215955 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an n X 4 array with new integer colors introduced in row major order.

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A215956 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nX5 array with new integer colors introduced in row major order.

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A215957 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nX6 array with new integer colors introduced in row major order.

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A215958 Number of horizontal, vertical and diagonal neighbor colorings of the even squares of an nX7 array with new integer colors introduced in row major order.

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