A360063 Triangle read by rows: T(m,n) is the number of Hamiltonian cycles in the graph whose nodes are the integer lattice points (x,y) with 0 <= x < m and 0 <= y < n, and with an edge between two nodes if there is no other integer lattice point on the line segment between them; 1 <= n <= m.

0, 0, 3, 0, 24, 1152, 0, 354, 436416, 2595450592, 0, 8138, 129422880

Offset

1,3

Comments

The graph represents tree-to-tree visibility in Euclid's orchard. It also appears in A247943, A247944, and A360062. Is there an established name for it?

Links

Table of n, a(n) for n=1..13.

Wikipedia, Euclid's orchard.

Example

Triangle begins:
  m\n| 1    2         3          4  5
  ---+-------------------------------
  1  | 0
  2  | 0    3
  3  | 0   24      1152
  4  | 0  354    436416 2595450592
  5  | 0 8138 129422880          ?  ?

Crossrefs

Cf. A247943, A247944, A321172, A360062.

Sequence in context: A013388 A344996 A057379 * A009777 A138543 A238104

Adjacent sequences: A360060 A360061 A360062 * A360064 A360065 A360066

Keyword

nonn,tabl,more

Author

Pontus von Brömssen, Jan 24 2023

Status

approved