cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

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.

Original entry on oeis.org

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

Views

Author

R. H. Hardin, Sep 04 2012

Keywords

Comments

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

Examples

			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

Links

Crossrefs

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

Programs

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

A286423 Number of matchings in the n X n white bishop graph.

Original entry on oeis.org

2, 7, 130, 4207, 1166928, 541240697, 2907639077764, 25886034363696809, 3341096345926174809912, 713738790204487208874991935, 2645105778378736719464340469683304, 16238808907214611705432043192158547965751
Offset: 2

Views

Author

Andrew Howroyd, May 08 2017

Keywords

Comments

Matchings are not necessarily perfect matchings.
C# software that can be used to compute this sequence can be found in A270228.

Links

Crossrefs

Cf. A286422, A287248, A270228, A216332 (independent vertex sets), A234630 (cycles).

A287248 Number of matchings in the n X n bishop graph.

Original entry on oeis.org

1, 4, 84, 16900, 39932844, 1361720957184, 774585118899294568, 8454365006540284439239696, 1984702974673190711327564424138048, 11162924792761237570313905721795529333447744, 1649914801339506800304019030963996680128410488784164960, 6996584578812582654135225585307693014250183123864863361126056356416, 919794116459365136444247186352581193250325236478988411540394596132809895149151936
Offset: 1

Views

Author

Eric W. Weisstein, May 22 2017

Keywords

Links

Crossrefs

Cf. A286422, A286423.

Formula

a(n) = A286422(n) * A286423(n). - Andrew Howroyd, May 23 2017

A297472 Number of maximal matchings in the n X n black bishop graph.

Original entry on oeis.org

1, 1, 5, 30, 1140, 69136, 33666336, 27406992000, 234805387040640, 3472530332565934080, 660908229459858361516032, 217930756388573091682145009664
Offset: 1

Views

Author

Eric W. Weisstein, Dec 30 2017

Keywords

Links

Crossrefs

Cf. A286422, A297471, A297490.

Extensions

a(7)-a(12) from Andrew Howroyd, Dec 30 2017
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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