A278826 - OEIS

%I #11 Nov 30 2016 01:19:08

%S -56,-48,-40,-32,-24,-16,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,16,

%T 24,32,40,48,56

%N Rook'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 rook 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 to some extent independent of the precise numbering scheme. For example, one could also use number = row + 8 * column, where row and column range from 1 to 8 (thus the numbers from 9 to 72), or from 0 to 7 (with squares numbered from 0 to 63). However, the board must be numbered such that moving up or down or left or right one square will always yield a difference of +- 8 or +- 1. (All directions mentioned here correspond to a standard vertical diagram with White starting at the bottom and Black starting on the top.)

%e If a rook moves two squares to the left, e.g., from h8 to f8, this yields a difference Y - X = -2.

%e If a rook moves three squares up, e.g., from h1 to h4, this yields a difference Y - X = 3*8 = 24.

%o (PARI) Set(concat(Vec([1,8]~*[-7..7][^8])))

%Y Cf. A278824 - A278828, A278829 (analog for Knights, ..., Kings and Pawns).

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

%K sign,easy,fini,full

%O 1,1

%A _M. F. Hasler_, Nov 28 2016