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A278828 King's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row. 5
-9, -8, -7, -1, 1, 7, 8, 9 (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 king stands on, and Y the number of a square to which it can move. 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 one row up yields a difference Y - X = +8. Moving one square diagonally down and right yields a difference Y - X = +1 - 8 = -7.
CROSSREFS
Cf. A278824 - A278827, A278829 (analog for Knights, ..., Queens and Pawns).
This is a subsequence of A278827: Queen's moves.
Sequence in context: A094145 A002388 A248080 * A334448 A011116 A106334
KEYWORD
sign,fini,full,easy
AUTHOR
M. F. Hasler, Nov 28 2016
STATUS
approved

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Last modified April 21 16:49 EDT 2024. Contains 371874 sequences. (Running on oeis4.)