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A278824 Knight moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row. 5
-17, -15, -10, -6, 6, 10, 15, 17 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Let the squares of a standard (8 X 8) chessboard be numbered sequentially from 1 to 64, row by row (e.g., a1 = 1, b1 = 2, ..., a2 = 9, ..., h8 = 64). Let X be the number of a square a knight stands on, and Y the number of a square to which it can jump. Then this sequence lists all possible values of Y-X.
The terms are independent of the precise numbering scheme, provided that the numbers of the four possible neighbors of a square differ by +- 1 in one direction and +- 8 in the other direction. For example, one could also use number = row + 8 * column, where row and column range from 1 to 8, or from 0 to 7.
LINKS
EXAMPLE
Moving two rows up and one to the left yields a difference Y - X = 2*8 - 1 = 15. Moving two squares to the right and one down yields a difference Y - X = 2 - 8 = -6.
CROSSREFS
Cf. A278825 - A278828, A278829 (analog for Bishops, ..., Kings and Pawns)
Sequence in context: A357190 A195534 A128158 * A085095 A004506 A096181
KEYWORD
sign,fini,easy,full
AUTHOR
M. F. Hasler, Nov 28 2016
STATUS
approved

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Last modified April 24 22:17 EDT 2024. Contains 371964 sequences. (Running on oeis4.)