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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

%I

%S 1,2,22,716,73346,23374544,23037365786,69630317879888

%N 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.

%C a(11) = 18267559028025887599256.

%e a(2) = 1;

%e +--*

%e | |

%e *--+

%e a(3) = 2;

%e +--*--* +--*

%e | | | |

%e *--+ * * +--*

%e | | | |

%e *--+ *--*--+

%e a(4) = 22;

%e +--*--*--* +--*--*--* +--*--*--*

%e | | | | | |

%e *--+--* * *--+--* * *--+--* *

%e | | | | | |

%e *--*--+ * *--+ * + *

%e | | | | | |

%e *--*--*--+ *--*--+ *--+

%e +--*--*--* +--*--*--* +--*--*--*

%e | | | | | |

%e *--+ *--* *--+ *--* *--+ *

%e | | | | | |

%e *--* +--* * +--* *--+ *

%e | | | | | |

%e *--*--*--+ *--*--+ *--+

%e +--*--*--* +--*--*--* +--*--*--*

%e | | | | | |

%e * +--*--* * +--* * * +--* *

%e | | | | | | | | | |

%e * *--+--* *--* + * * * + *

%e | | | | | | | |

%e *--*--*--+ *--+ *--* *--+

%e +--*--* +--*--* +--*--*

%e | | | | | |

%e *--+ *--* *--+ * *--+ *

%e | | | | | |

%e *--+ * *--* +--* * +--*

%e | | | | | |

%e *--+ *--*--*--+ *--*--+

%e +--*--* +--* *--* +--* *--*

%e | | | | | | | | | |

%e * +--* * +--* * * +--* *

%e | | | | | |

%e * *--+--* *--*--+ * * *--+ *

%e | | | | | | | |

%e *--*--*--+ *--+ *--* *--+

%e +--* *--* +--* +--*

%e | | | | | | | |

%e * + * * * +--*--* * +--*--*

%e | | | | | | | |

%e * *--+ * *--*--+ * * *--+ *

%e | | | | | | | |

%e *--*--*--+ *--+ *--* *--+

%e +--* +--* +--*

%e | | | | | |

%e * +--* * +--* * + *--*

%e | | | | | | | |

%e *--* +--* * +--* * *--+ *

%e | | | | | |

%e *--*--+ *--*--*--+ *--*--*--+

%e +--*

%e | |

%e * +

%e | |

%e * *--+--*

%e | |

%e *--*--*--+

%o (Python)

%o # Using graphillion

%o from graphillion import GraphSet

%o import graphillion.tutorial as tl

%o def A333796(n):

%o universe = tl.grid(n - 1, n - 1)

%o GraphSet.set_universe(universe)

%o cycles = GraphSet.cycles()

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

%o for i in points:

%o cycles = cycles.including(i)

%o return cycles.len()

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

%Y Cf. A333455, A333464, A333466, A333795.

%K nonn,more

%O 2,2

%A _Seiichi Manyama_, Apr 05 2020

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Last modified September 20 11:38 EDT 2021. Contains 347584 sequences. (Running on oeis4.)