A216338 -id:A216338 - cp's OEIS frontend

A216332 Number of horizontal and antidiagonal neighbor colorings of the even squares of an n X 2 array with new integer colors introduced in row major order.

1, 2, 3, 10, 27, 114, 409, 2066, 9089, 52922, 272947, 1788850, 10515147, 76282138, 501178937, 3974779402, 28773452321, 247083681522, 1949230218691, 17984917069018, 153281759047387, 1510073008031682, 13806215066685433

Offset: 1

R. H. Hardin, Sep 04 2012

nonn

Number of vertex covers and independent vertex sets of the n-1 X n-1 black bishops graph. Equivalently, the number of ways to place any number of non-attacking bishops on the black squares of an n-1 X n-1 board. - Andrew Howroyd, May 08 2017

			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..0....x..1....x..1....x..0....x..1....x..1....x..0
..0..x....2..x....2..x....1..x....2..x....2..x....1..x....2..x....0..x....1..x
..x..2....x..0....x..1....x..2....x..1....x..0....x..1....x..0....x..1....x..2
..3..x....3..x....3..x....0..x....2..x....1..x....0..x....2..x....0..x....3..x
There are 5 black squares on a 3 X 3 board. There is 1 way to place no non-attacking bishops, 5 ways to place 1 and 4 ways to place 2 so a(4)=1+5+4=10. - _Andrew Howroyd_, Jun 06 2017

R. H. Hardin, Table of n, a(n) for n = 1..210
Eric Weisstein's World of Mathematics, Black Bishop Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover

Column 2 of A216338.
Row sums of A274105(n-1) for n>2.
Cf. A216078, A201862, A286422.

Table[Sum[Binomial[Ceiling[n/2], k] BellB[n - k], {k, 0, Ceiling[n/2]}], {n, 0, 20}] (* Eric W. Weisstein, Jun 25 2017 *)

A216333 Number of horizontal 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, 2, 15, 52, 877, 4140, 115975, 678570, 27644437, 190899322, 10480142147, 82864869804, 5832742205057, 51724158235372, 4506715738447323, 44152005855084346, 4638590332229999353, 49631246523618756274

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Column 3 of A216338

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

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

A216334 Number of horizontal and antidiagonal 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, 5, 42, 726, 15144, 502658, 18378580, 950376664, 52183667212, 3788883495864, 286529186194664, 27420871472654064, 2701657928740913416, 326508788572113365896, 40316833236311531705440, 5965422648942609379676752, 897057171450298448594594368, 158723597386944654236759074832

Offset: 1

R. H. Hardin, Sep 04 2012

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..78

Column 4 of A216338.

A216335 Number of horizontal and antidiagonal neighbor colorings of the even squares of an n X 5 array with new integer colors introduced in row major order.

Original entry on oeis.org

2, 12, 602, 12840, 2387180, 99827160, 41521045376, 2751754706832, 2063225889204272, 194478305002268064, 232628053298868289568, 29191372156840204219200, 51464654047934299798487552

Offset: 1

R. H. Hardin, Sep 04 2012

nonn

Column 5 of A216338.

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

R. H. Hardin, Table of n, a(n) for n = 1..49

Cf. A216338.

A216336 Number of horizontal and antidiagonal 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, 42, 2440, 373780, 87852160, 37060650272, 20358402201792, 17131843186425504, 17423570614012565376, 24860319276726031245440, 41082882676098706722895360, 90015726535715347904300537088, 222247072052822589353800809064448

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Column 6 of A216338

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

R. H. Hardin, Table of n, a(n) for n = 1..26

A216337 Number of horizontal 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, 136, 61915, 12297870, 33093354906, 18383343930862, 148049849072167133, 166176901557427161788, 2985013124775648539788601, 5737167226254078112766902750, 194564626464285317322710261641286

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Column 7 of A216338

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

R. H. Hardin, Table of n, a(n) for n = 1..17

A216339 Number of horizontal 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, 3, 15, 42, 602, 2440, 61915, 322776, 12297978, 77360796, 4044784633, 29562890886, 2004648242718, 16604827619828, 1404640885455993, 12954736337254696, 1328741141974378250, 13465808369740333664

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Row 3 of A216338

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

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

A216340 Number of horizontal 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, 10, 52, 726, 12840, 373780, 12297870, 580853761, 29562890980, 2004648246554, 142953068558998, 12954739605661928, 1216988850964527370, 140585911310155419266, 16679506383419809650408, 2374936932537133281235971

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Row 4 of A216338

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A216331 Number of horizontal 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, 2, 15, 726, 2387180, 37060650272, 148049849072167133, 2765650089185458968363718

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Diagonal of A216338

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

A216341 Number of horizontal 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, 27, 877, 15144, 2387180, 87852160, 33093354906, 2004646634218, 1404640885994156, 123560104158582188, 140585911310274456089

Offset: 1

R. H. Hardin Sep 04 2012

nonn

Row 5 of A216338

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

cp's OEIS Frontend

A216332 Number of horizontal and antidiagonal 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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A216333 Number of horizontal 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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A216334 Number of horizontal and antidiagonal 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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A216335 Number of horizontal and antidiagonal neighbor colorings of the even squares of an n X 5 array with new integer colors introduced in row major order.

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A216336 Number of horizontal and antidiagonal neighbor colorings of the even squares of an nX6 array with new integer colors introduced in row major order.

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A216337 Number of horizontal 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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A216339 Number of horizontal 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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A216340 Number of horizontal 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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A216331 Number of horizontal 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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A216341 Number of horizontal 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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