A347363 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,3`
	COMMENTS	`If we enumerate the squares in the 3 X n board like this:` `------------------------------------` `\| 1 \| 4 \| 7 \| 10 \| 13 \| ... \| 3n-2 \|` `------------------------------------` `\| 2 \| 5 \| 8 \| 11 \| 14 \| ... \| 3n-1 \|` `------------------------------------` `\| 3 \| 6 \| 9 \| 12 \| 15 \| ... \| 3n \|` `------------------------------------` `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`

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Last modified August 29 18:55 EDT 2024. Contains 375518 sequences. (Running on oeis4.)