A270247 -id:A270247 - cp's OEIS frontend

A222199 Number of Hamiltonian cycles in the graph C_n X C_n.

48, 1344, 23580, 3273360, 257165468, 171785923808, 61997157648756, 196554899918485160

Offset: 3

N. J. A. Sloane, Feb 14 2013

C_n X C_n is also known as the (n,n)-torus grid graph.

Artem M. Karavaev, Hamilton Cycles.
Eric Weisstein's World of Mathematics, Hamiltonian Cycle.
Eric Weisstein's World of Mathematics, Torus Grid Graph.

Cf. A270273, A003763, A222197, A268838, A222198, A193153, A270247.

Table[Length[FindHamiltonianCycle[GraphProduct[CycleGraph[n], CycleGraph[n], "Cartesian"], All]], {n, 3, 6}] (* Eric W. Weisstein, Dec 16 2023 *)

A270246 Array read by antidiagonals: T(n,m) is the number of matchings in the torus grid graph C_n X C_m.

Original entry on oeis.org

1, 2, 2, 4, 7, 4, 7, 32, 32, 7, 11, 108, 370, 108, 11, 18, 342, 2764, 2764, 342, 18, 29, 1104, 19874, 41025, 19874, 1104, 29, 47, 3544, 144108, 576287, 576287, 144108, 3544, 47, 76, 11396, 1043060, 8205424, 15637256, 8205424, 1043060, 11396, 76

Offset: 1

Andrew Howroyd, Mar 13 2016

			The start of the sequence as table:
*   1    2      4       7        11          18 ...
*   2    7     32     108       342        1104 ...
*   4   32    370    2764     19874      144108 ...
*   7  108   2764   41025    576287     8205424 ...
*  11  342  19874  576287  15637256   430996378 ...
*  18 1104 144108 8205424 430996378 23079663560 ...
* ...

Andrew Howroyd, Table of n, a(n) for n = 1..284
Eric Weisstein's World of Mathematics, Independent Edge Set
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Torus Grid Graph

Main diagonal is A270247. Row 2 is A102080.

T(1, m) = A000032(m) for m<>2.

cp's OEIS Frontend

A222199 Number of Hamiltonian cycles in the graph C_n X C_n.

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