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 1-5 of 5 results.

A286418 Array read by antidiagonals: T(n,m) is the number of (undirected) cycles in the rook graph K_n X K_m.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 7, 14, 14, 7, 37, 170, 312, 170, 37, 197, 2904, 13945, 13945, 2904, 197, 1172, 74779, 1241696, 3228524, 1241696, 74779, 1172, 8018, 2751790, 196846257, 1723178763, 1723178763, 196846257, 2751790, 8018
Offset: 1

Views

Author

Andrew Howroyd, May 08 2017

Keywords

Examples

			Table starts:
================================================
m\n  1    2       3          4             5
--+---------------------------------------------
1 |  0    0       1          7            37 ...
2 |  0    1      14        170          2904 ...
3 |  1   14     312      13945       1241696 ...
4 |  7  170   13945    3228524    1723178763 ...
5 | 37 2904 1241696 1723178763 6198979538330 ...
  ...

Links

Crossrefs

Main diagonal is A234624.
Columns 1..3 are A002807, A341500, A341501.
Cf. A269562, A269565.

A234603 Numbers of undirected cycles in the n X n black bishop graph.

Original entry on oeis.org

2, 53, 12424, 12300529, 504040211574, 84649132742336262, 1080241691057266946999792
Offset: 3

Views

Author

Eric W. Weisstein, Dec 28 2013

Keywords

Links

Crossrefs

Cf. A234630, A234636, A234624, A282889, A234632.

Extensions

a(7) from Eric W. Weisstein, Jan 04 2014
a(3) prepended and a(8)-a(9) from Andrew Howroyd, May 08 2017

A234630 Numbers of undirected cycles in the n X n white bishop graph.

Original entry on oeis.org

1, 53, 4943, 12300529, 134480655082, 84649132742336262, 212615053823090089357638
Offset: 3

Views

Author

Eric W. Weisstein, Dec 28 2013

Keywords

Links

Crossrefs

Cf. A234603, A234636, A234624, A282890, A234637.

Extensions

a(7) from Eric W. Weisstein, Jan 04 2014
a(3) prepended and a(8)-a(9) from Andrew Howroyd, May 08 2017

A360854 Number of induced cycles in the n X n rook graph.

Original entry on oeis.org

0, 1, 21, 236, 4040, 114105, 4662721, 256485936, 18226110456, 1623855703785, 177195820502965, 23237493232958796, 3605437233380103056, 653193551573628910481, 136634950180317224879985, 32681589590709963123110080, 8863149183726257535369656976
Offset: 1

Views

Author

Andrew Howroyd, Feb 24 2023

Keywords

Comments

Induced cycles are sometimes called chordless cycles (but some definitions require chordless cycles to have a cycle length of at least 4). See A070968 for the version that excludes triangles.

Links

Crossrefs

Main diagonal of A360853.
Cf. A070968, A234624, A288961, A360852.

Programs

  • PARI
    a(n) = 2*n*binomial(n,3) + sum(k=2, n, binomial(n,k)^2 * k! * (k-1)!)/2

Formula

a(n) = A288961(n) + A070968(n).
a(n) = 2*n*binomial(n,3) + Sum_{k=2..n} binomial(n,k)^2 * k! * (k-1)! / 2.

A288967 Number of (undirected) paths on the n X n rook graph.

Original entry on oeis.org

0, 12, 4536, 111933456
Offset: 1

Views

Author

Eric W. Weisstein, Jun 20 2017

Keywords

Links

  • Eric Weisstein's World of Mathematics, Graph Path
  • Eric Weisstein's World of Mathematics, Rook Graph

Crossrefs

Main diagonal of A360877.
Cf. A096970, A234624.
Showing 1-5 of 5 results.

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

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