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 1-8 of 8 results.

A268838 Number of (undirected) Hamiltonian paths in the torus grid graph C_n X C_n.

Original entry on oeis.org

1, 4, 756, 45696, 2955700, 560028096, 126412047692, 93784124187136
Offset: 1

Views

Author

Andrew Howroyd, Feb 14 2016

Keywords

Comments

Here, X (sometimes also written \square) is the graph Cartesian product.

Crossrefs

A270273 Array read by antidiagonals: T(n,m) = number of Hamiltonian cycles in C_n X C_m.

Original entry on oeis.org

0, 0, 0, 1, 1, 1, 1, 3, 3, 1, 1, 6, 48, 6, 1, 1, 5, 126, 126, 5, 1, 1, 8, 390, 1344, 390, 8, 1, 1, 7, 1014, 2930, 2930, 1014, 7, 1, 1, 10, 2982, 28060, 23580, 28060, 2982, 10, 1, 1, 9, 8094, 55230, 145210, 145210, 55230, 8094, 9, 1
Offset: 1

Views

Author

Andrew Howroyd, Mar 14 2016

Keywords

Examples

			The start of the sequence as table:
  0 0    1     1       1        1         1 ...
  0 1    3     6       5        8         7 ...
  1 3   48   126     390     1014      2982 ...
  1 6  126  1344    2930    28060     55230 ...
  1 5  390  2930   23580   145210   1045940 ...
  1 8 1014 28060  145210  3273360  16111928 ...
  1 7 2982 55230 1045940 16111928 257165468 ...
  ...
		

Crossrefs

Row n=3-5 give: A194952, A216588, A358853.
Main diagonal gives A222199.

Formula

T(n,2) = A124349(n) / 2.

A296527 Number of (undirected) cycles in the n X n torus grid graph.

Original entry on oeis.org

312, 14704, 2183490, 995818716, 1383238940818, 5846378997135040, 75162787766308673244
Offset: 3

Views

Author

Eric W. Weisstein, Dec 14 2017

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Length[FindCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], Infinity, All]], {n, 3, 5}] (* Eric W. Weisstein, Dec 16 2023 *)
  • Python
    # Using graphillion
    from graphillion import GraphSet
    def make_CnXCk(n, k):
        grids = []
        for i in range(1, k + 1):
            for j in range(1, n):
                grids.append((i + (j - 1) * k, i + j * k))
            grids.append((i + (n - 1) * k, i))
        for i in range(1, k * n, k):
            for j in range(1, k):
                grids.append((i + j - 1, i + j))
            grids.append((i + k - 1, i))
        return grids
    def A296527(n):
        universe = make_CnXCk(n, n)
        GraphSet.set_universe(universe)
        cycles = GraphSet.cycles()
        return cycles.len()
    print([A296527(n) for n in range(3, 7)])  # Seiichi Manyama, Nov 22 2020

Extensions

a(7) from Andrew Howroyd, Dec 14 2017
a(8)-a(9) from Ed Wynn, Jun 28 2023

A269561 Number of (undirected) Hamiltonian cycles in the n X n rook graph K_n X K_n.

Original entry on oeis.org

1, 48, 284112, 335750676480, 112249362914249932800, 14994936423694913432308324761600
Offset: 2

Views

Author

Andrew Howroyd, Feb 29 2016

Keywords

Crossrefs

Extensions

Name adjusted by Eric W. Weisstein, May 06 2019

A358853 Number of Hamiltonian cycles in C_5 X C_n.

Original entry on oeis.org

20, 390, 2930, 23580, 145210, 1045940, 6228730, 43322370, 260600210, 1776654220, 10913989610, 73525916750, 461264468640, 3088176680560, 19722405442490, 131703577902460, 853035459491710, 5693694272274220, 37271158654667390, 248902943147007900
Offset: 2

Views

Author

Seiichi Manyama, Dec 03 2022

Keywords

Crossrefs

Row 5 of A270273.
Cf. A222199.

Extensions

More terms from Ed Wynn, Jun 25 2023

A270247 Number of matchings in the n X n torus grid graph C_n X C_n.

Original entry on oeis.org

1, 7, 370, 41025, 15637256, 23079663560, 127193770624285, 2645142169931308801, 206932904585998805434690, 60953421285412135689567940992, 67583556205239600880061198746186383, 282092296203355454009618109524478429807744
Offset: 1

Views

Author

Andrew Howroyd, Mar 13 2016

Keywords

Comments

C_{n} X C_{n} is also known as the (n,n)-torus grid graph.

Crossrefs

A222198 Order of linear recurrence for number of Hamiltonian cycles in the graph C_n X C_k as a function of k.

Original entry on oeis.org

6, 28, 84, 257, 856, 2785
Offset: 3

Views

Author

N. J. A. Sloane, Feb 14 2013

Keywords

Crossrefs

Cf. A222199.

A297669 Number of chordless cycles in the n X n torus grid graph.

Original entry on oeis.org

15, 224, 1815, 28716, 886837, 46775584, 4207536351
Offset: 3

Views

Author

Eric W. Weisstein, Jan 02 2018

Keywords

Crossrefs

Extensions

a(6)-a(9) from Andrew Howroyd, Jan 08 2018
Showing 1-8 of 8 results.