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.

A096970 Number of ways to number the cells of an n X n square grid with 1,2,3,...,n^2 so that successive integers are in the same row or column.

Original entry on oeis.org

1, 8, 1512, 22394880, 50657369241600, 28606505102329400524800, 5959275438217048853558620520448000
Offset: 1

Views

Author

John W. Layman, Jul 16 2004

Keywords

Comments

Suggested by Leroy Quet, Jul 05 2004.
For n >= 2, number of (directed) Hamiltonian paths on the n X n rook graph. - Eric W. Weisstein, Dec 16 2013

Examples

			Among the 4 X 4 grids counted is:
1   2  3 10
15  6  5 11
14 13  4 12
16  7  8  9

Links

Crossrefs

Cf. A096969, A269561, A269565.

Extensions

a(5) from Eric W. Weisstein, Dec 28 2013
a(6)-a(7) from Andrew Howroyd, Feb 29 2016

A269562 Array read by antidiagonals: T(n,m) is the number of Hamiltonian cycles in the rook graph K_n X K_m.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 3, 3, 3, 3, 12, 30, 48, 30, 12, 60, 480, 1566, 1566, 480, 60, 360, 12000, 126120, 284112, 126120, 12000, 360, 2520, 430920, 18153720, 122330880, 122330880, 18153720, 430920, 2520, 20160, 21052080, 4357332000, 112777827840, 335750676480, 112777827840, 4357332000, 21052080, 20160
Offset: 1

Views

Author

Andrew Howroyd, Feb 29 2016

Keywords

Comments

Equivalently, the number of rook tours on an n X m lattice.
2*T(n,m) is divisible by (n-1)!*(m-1)!. - Andrew Howroyd, Feb 08 2021

Examples

			Array begins:
=============================================================
n\m |   1      2          3            4                5
----+--------------------------------------------------------
  1 |   0      0          1            3               12 ...
  2 |   0      1          3           30              480 ...
  3 |   1      3         48         1566           126120 ...
  4 |   3     30       1566       284112        122330880 ...
  5 |  12    480     126120    122330880     335750676480 ...
  6 |  60  12000   18153720 112777827840 2190773906150400 ...
  7 | 360 430920 4357332000 ...
     ...

Links

Crossrefs

Column 1 is A001710(n-1) for n >= 3.
Columns 2..4 are A276356, A341498, A341499.
Main diagonal is A269561.
Cf. A269565, A286418.

Formula

From Andrew Howroyd, Feb 08 2021: (Start)
T(n,m) = T(m,n).
T(n,1) = (n-1)!/2 for n >= 3. (End)

A270228 Number of matchings in the n X n rook graph K_n X K_n.

Original entry on oeis.org

1, 7, 370, 270529, 3337807996, 855404716021831, 5352265402523357926168, 940288991338542314571521981185, 5236753179470435264288904589157765055760, 1029720447530443779943631183186535523331685533812231
Offset: 1

Views

Author

Andrew Howroyd, Mar 13 2016

Keywords

Comments

K_n X K_n is also called the rook graph or lattice graph.

Links

Crossrefs

Cf. A270227, A270229, A085537 (Wiener index), A002720 (independent vertex sets), A269561, A028420.

A234624 Number of (undirected) cycles in the n X n rook graph.

Original entry on oeis.org

0, 1, 312, 3228524, 6198979538330, 3366323909717796339009
Offset: 1

Views

Author

Eric W. Weisstein, Dec 28 2013

Keywords

Links

Crossrefs

Main diagonal of A286418.
Cf. A269561, A096970.

Extensions

a(6) from Andrew Howroyd, May 08 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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