A180504 Number of Hamiltonian cycles in P_10 X P_n.

0, 1, 16, 1517, 18684, 1024028, 17066492, 681728204, 13916993782, 467260456608, 10754797724124, 328076475659033, 8091313110371792, 233977398720987284, 6002042996016384360, 168435972906750526954, 4418118886987754341770, 121913396076344218930045

Offset

1,3

Comments

The linear recurrence for this sequence has order 346. It is too large to be posted here.

Links

Huaide Cheng, Table of n, a(n) for n = 1..700 (terms 1..100 from Andrew Howroyd)

Pablo Blanco and Doron Zeilberger, Counting (and Randomly Generating) Hamiltonian Cycles in Rectangular Grids, arXiv:2603.24315 [math.CO], 2026. See references.

Flow Problem, Hamilton Cycles (see Maple worksheet).

A. Kloczkowski and R. L. Jernigan, Transfer matrix method for enumeration and generation of compact self-avoiding walks. I. Square lattices, J. Chem. Phys., 109 (1998), 5134-5146. See Table IV, column m = 10.

Index entries for sequences related to graphs, Hamiltonian

Index entries for linear recurrences with constant coefficients, order 346.

Crossrefs

Row/column 10 of A321172.

Cf. A160149.

Sequence in context: A396492 A302116 A294163 * A178024 A221613 A266156

Adjacent sequences: A180501 A180502 A180503 * A180505 A180506 A180507

Keyword

nonn

Author

Artem M. Karavaev, Sep 09 2010

Extensions

a(16) onwards from Andrew Howroyd, Dec 13 2024

Status

approved