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A333796 Number of self-avoiding closed paths on an n X n grid which pass through all points on the diagonal connecting NW and SE corners. 2
1, 2, 22, 716, 73346, 23374544, 23037365786, 69630317879888 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

a(11) = 18267559028025887599256.

LINKS

Table of n, a(n) for n=2..9.

EXAMPLE

a(2) = 1;

   +--*

   |  |

   *--+

a(3) = 2;

   +--*--*   +--*

   |     |   |  |

   *--+  *   *  +--*

      |  |   |     |

      *--+   *--*--+

a(4) = 22;

   +--*--*--*   +--*--*--*   +--*--*--*

   |        |   |        |   |        |

   *--+--*  *   *--+--*  *   *--+--*  *

         |  |         |  |         |  |

   *--*--+  *      *--+  *         +  *

   |        |      |     |         |  |

   *--*--*--+      *--*--+         *--+

   +--*--*--*   +--*--*--*   +--*--*--*

   |        |   |        |   |        |

   *--+  *--*   *--+  *--*   *--+     *

      |  |         |  |         |     |

   *--*  +--*      *  +--*      *--+  *

   |        |      |     |         |  |

   *--*--*--+      *--*--+         *--+

   +--*--*--*   +--*--*--*   +--*--*--*

   |        |   |        |   |        |

   *  +--*--*   *  +--*  *   *  +--*  *

   |  |         |  |  |  |   |  |  |  |

   *  *--+--*   *--*  +  *   *  *  +  *

   |        |         |  |   |  |  |  |

   *--*--*--+         *--+   *--*  *--+

   +--*--*      +--*--*      +--*--*

   |     |      |     |      |     |

   *--+  *--*   *--+  *      *--+  *

      |     |      |  |         |  |

      *--+  *   *--*  +--*      *  +--*

         |  |   |        |      |     |

         *--+   *--*--*--+      *--*--+

   +--*--*      +--*  *--*   +--*  *--*

   |     |      |  |  |  |   |  |  |  |

   *  +--*      *  +--*  *   *  +--*  *

   |  |         |        |   |        |

   *  *--+--*   *--*--+  *   *  *--+  *

   |        |         |  |   |  |  |  |

   *--*--*--+         *--+   *--*  *--+

   +--*  *--*   +--*         +--*

   |  |  |  |   |  |         |  |

   *  +  *  *   *  +--*--*   *  +--*--*

   |  |  |  |   |        |   |        |

   *  *--+  *   *--*--+  *   *  *--+  *

   |        |         |  |   |  |  |  |

   *--*--*--+         *--+   *--*  *--+

   +--*         +--*         +--*

   |  |         |  |         |  |

   *  +--*      *  +--*      *  +  *--*

   |     |      |     |      |  |  |  |

   *--*  +--*   *     +--*   *  *--+  *

      |     |   |        |   |        |

      *--*--+   *--*--*--+   *--*--*--+

   +--*

   |  |

   *  +

   |  |

   *  *--+--*

   |        |

   *--*--*--+

PROG

(Python)

# Using graphillion

from graphillion import GraphSet

import graphillion.tutorial as tl

def A333796(n):

    universe = tl.grid(n - 1, n - 1)

    GraphSet.set_universe(universe)

    cycles = GraphSet.cycles()

    points = [i + 1 for i in range(n * n) if i % n - i // n == 0]

    for i in points:

        cycles = cycles.including(i)

    return cycles.len()

print([A333796(n) for n in range(2, 10)])

CROSSREFS

Cf. A333455, A333464, A333466, A333795.

Sequence in context: A308535 A318639 A220732 * A132568 A279802 A015210

Adjacent sequences:  A333793 A333794 A333795 * A333797 A333798 A333799

KEYWORD

nonn,more

AUTHOR

Seiichi Manyama, Apr 05 2020

STATUS

approved

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Last modified July 29 22:26 EDT 2021. Contains 346346 sequences. (Running on oeis4.)