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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A358796 Number of Hamiltonian paths in P_9 X P_n.

Original entry on oeis.org

1, 74, 3190, 122188, 2434670, 82550864, 1449655468, 43551685370, 745416341496, 20458460935162, 350662618941136, 8977863552693182, 155527664975367738, 3769078188330226854, 66168756974349933990, 1534449253192384210354, 27299151102034089996326, 610935315274446987589872
Offset: 1

Views

Author

Seiichi Manyama, Dec 01 2022

Keywords

Links

Crossrefs

Row n=9 of A332307.

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 27 2023

A366399 Triangle read by rows: T(n,k) is the number of paths traveling orthogonally on an n X k grid that visit every cell.

Original entry on oeis.org

1, 1, 4, 1, 8, 20, 1, 14, 62, 276, 1, 22, 132, 1006, 4324, 1, 32, 336, 3610, 26996, 229348, 1, 44, 688, 12010, 109722, 1620034, 13535280, 1, 58, 1578, 38984, 602804, 12071462, 175905310, 3023313284, 1, 74, 3190, 122188, 2434670, 82550864, 1449655468, 43551685370, 745416341496
Offset: 1

Views

Author

Douglas Boffey, Oct 09 2023

Keywords

Examples

			T(n,k) is a triangular array read by rows:
  1,
  1,  4,
  1,  8, 20,
  1, 14, 62, 276,
  ...
T(2,2) = 4:
  +---+---+  +---+---+  +---+---+  +---+---+
  |   |   |  |   |   |  |   |   |  |   |   |
  | **|** |  | * | * |  | **|** |  | **|** |
  |   | * |  | * | * |  | * |   |  | * | * |
  +---+---+  +---+---+  +---+---+  +---+---+
  |   | * |  | * | * |  | * |   |  | * | * |
  | **|** |  | **|** |  | **|** |  | * | * |
  |   |   |  |   |   |  |   |   |  |   |   |
  +---+---+  +---+---+  +---+---+  +---+---+

Crossrefs

See A332307 for another version.
Cf. A120443 (T(n,n)), A366411 (row sums).

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Douglas Boffey, Oct 09 2023

Keywords

Examples

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

Crossrefs

Row sums of triangle A366399.

Extensions

More terms (using A332307) from Pontus von Brömssen, Oct 09 2023
Previous Showing 11-13 of 13 results.

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