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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

%I #13 Nov 30 2016 01:16:28

%S -9,-8,-7,-1,1,7,8,9

%N King's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row.

%C 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.

%C 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.

%e 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.

%Y Cf. A278824 - A278827, A278829 (analog for Knights, ..., Queens and Pawns).

%Y This is a subsequence of A278827: Queen's moves.

%K sign,fini,full,easy

%O 1,1

%A _M. F. Hasler_, Nov 28 2016

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