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 A333515 Number of self-avoiding closed paths on an n X 5 grid which pass through four corners ((0,0), (0,4), (n-1,4), (n-1,0)). 3

%I

%S 1,7,49,373,3105,26515,227441,1953099,16782957,144262743,1240194297,

%T 10662034451,91663230249,788046822891,6775004473757,58246174168047,

%U 500755017859261,4305100014182879,37011883913816129,318199242452585915,2735628331213604009,23518793814422304163

%N Number of self-avoiding closed paths on an n X 5 grid which pass through four corners ((0,0), (0,4), (n-1,4), (n-1,0)).

%C Also number of self-avoiding closed paths on a 5 X n grid which pass through four corners ((0,0), (0,n-1), (4,n-1), (4,0)).

%H Seiichi Manyama, <a href="/A333515/b333515.txt">Table of n, a(n) for n = 2..1000</a>

%e a(2) = 1;

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

%e | |

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

%e a(3) = 7;

%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 A333513(n, k):

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

%o GraphSet.set_universe(universe)

%o cycles = GraphSet.cycles()

%o for i in [1, k, k * (n - 1) + 1, k * n]:

%o cycles = cycles.including(i)

%o return cycles.len()

%o def A333515(n):

%o return A333513(n, 5)

%o print([A333515(n) for n in range(2, 25)])

%Y Column k=5 of A333513.

%K nonn

%O 2,2

%A _Seiichi Manyama_, Mar 25 2020

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Last modified March 31 11:40 EDT 2023. Contains 361648 sequences. (Running on oeis4.)