A366411 a(n) is the total number of Hamiltonian paths on rectangular grids of size n X k for 1 <= k <= n.

1, 5, 29, 353, 5485, 260323, 15277779, 3211933481, 790502793321, 751204032996623, 808973740240335345, 3499358510266725179221, 16872857815987642169925097, 333905047994165804391613820789, 7308582206982080422190512432243395

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Example

For n = 2, the a(2) = 5 solutions are:
  +---+  +---+---+  +---+---+  +---+---+  +---+---+
  |   |  |   |   |  |   |   |  |   |   |  |   |   |
  | * |  | **|** |  | * | * |  | **|** |  | **|** |
  | * |  |   | * |  | * | * |  | * |   |  | * | * |
  +---+  +---+---+  +---+---+  +---+---+  +---+---+
  | * |  |   | * |  | * | * |  | * |   |  | * | * |
  | * |  | **|** |  | **|** |  | **|** |  | * | * |
  |   |  |   |   |  |   |   |  |   |   |  |   |   |
  +---+  +---+---+  +---+---+  +---+---+  +---+---+

Crossrefs

Row sums of triangle A366399.

Sequence in context: A195228 A226668 A226666 * A356486 A289483 A216027

Adjacent sequences: A366408 A366409 A366410 * A366412 A366413 A366414

Keyword

nonn,walk,more

Author

Douglas Boffey, Oct 09 2023

Extensions

More terms (using A332307) from Pontus von Brömssen, Oct 09 2023

Status

approved