A333246 - OEIS

%I #114 Jan 31 2022 03:14:52

%S 1,7,97,4111,532269,212372937,263708907211,1013068026356375,

%T 11955420069208095719,432101605951906251627393,

%U 47778407166747833830058004149,16149888968763663448192636077980753,16675786862526496319891707194153887550751,52568166380872328447478940416604864445574575709

%N Number of self-avoiding closed paths on an n X n grid which pass through NW corner.

%F a(n) = A333439(n) - 1 for n > 1.

%e a(2) = 1;

%e    +--*

%e    |  |

%e    *--*

%e a(3) = 7;

%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 A333246(n):

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

%o     GraphSet.set_universe(universe)

%o     cycles = GraphSet.cycles().including(1)

%o     return cycles.len()

%o print([A333246(n) for n in range(2, 10)])

%Y Cf. A140517, A333247, A333323, A333438, A333439, A333466.

%K nonn

%O 2,2

%A _Seiichi Manyama_, Mar 23 2020

%E a(11), a(13) from _Seiichi Manyama_, Apr 07 2020

%E a(10), a(12), a(14)-a(15) from _Andrew Howroyd_, Jan 30 2022