%I #13 Nov 30 2016 01:19:29
%S 63,56,54,49,48,45,42,40,36,35,32,28,27,24,21,18,16,
%T 14,9,8,7,6,5,4,3,2,1,1,2,3,4,5,6,7,8,9,14,16,18,21,24,27,
%U 28,32,35,36,40,42,45,48,49,54,56,63
%N Queen'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 queen stands on, and Y the number of a square to which it can move. Then this sequence lists all possible values of YX.
%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.)
%F Equal to A278825 union A278826 (Bishop's and Rook's moves).
%e If a queen moves two squares to the left, e.g., from h8 to f8, this yields a difference Y  X = 2.
%e If a queen moves three squares up, e.g., from h1 to h4, this yields a difference Y  X = 3*8 = 24.
%o (PARI) Set(concat(Vec([1,7,8,9]~*[7..7][^8])))
%Y Cf. A278824  A278828, A278829 (analog for Knights, ..., Kings and Pawns).
%Y Contains all of A278825, A278826, A278828 and A278829 as a subsequence.
%K sign,easy,fini,full
%O 1,1
%A _M. F. Hasler_, Nov 28 2016
