A347363 Number of self-avoiding knight's paths from the lower left corner to the lower right corner of a 3 X n chessboard.

1, 0, 2, 8, 32, 156, 871, 5292, 28702, 154162, 845532, 4662014, 25579463, 140098348, 767973001, 4212065280, 23097682805, 126643657272, 694390484065, 3807499106946, 20877386149018, 114474503105178, 627683328355315, 3441701959286326, 18871492466212538

Offset

1,3

Comments

If we enumerate the squares in the 3 X n board like this:

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| 1 | 4 | 7 | 10 | 13 | ... | 3n-2 |

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| 2 | 5 | 8 | 11 | 14 | ... | 3n-1 |

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| 3 | 6 | 9 | 12 | 15 | ... | 3n |

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then a(n) is the number of self-avoiding knight's paths on such a board from square 3 to square 3n.

Links

Table of n, a(n) for n=1..25.

Example

For n = 4 we have exactly 8 self-avoiding paths starting at square 3 and ending at square 12:
  3,  4,  9, 10,  5, 12;
  3,  4,  9,  2,  7, 12;
  3,  8,  1,  6,  7, 12;
  3,  4, 11,  6,  7, 12;
  3,  8,  1,  6, 11,  4,  9,  2,  7, 12;
  3,  4, 11,  6,  7,  2,  9, 10,  5, 12;
  3,  8,  1,  6,  7,  2,  9, 10,  5, 12;
  3,  8,  1,  6, 11,  4,  9, 10,  5, 12;

Crossrefs

Cf. A118067, A169696, A212715.

Sequence in context: A054116 A348905 A131785 * A359398 A006669 A193778

Adjacent sequences: A347360 A347361 A347362 * A347364 A347365 A347366

Keyword

nonn,walk

Author

Andrzej Kukla, Aug 29 2021

Extensions

a(8)-a(15) from Pontus von Brömssen, Aug 30 2021

Terms a(16) and beyond from Andrew Howroyd, Nov 19 2021

Status

approved