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%I #14 Nov 30 2016 01:18:36
%S -17,-15,-10,-6,6,10,15,17
%N Knight 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 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.
%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 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.
%Y Cf. A278825 - A278828, A278829 (analog for Bishops, ..., Kings and Pawns)
%K sign,fini,easy,full
%O 1,1
%A _M. F. Hasler_, Nov 28 2016
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