

A278827


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


4



63, 56, 54, 49, 48, 45, 42, 40, 36, 35, 32, 28, 27, 24, 21, 18, 16, 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, 28, 32, 35, 36, 40, 42, 45, 48, 49, 54, 56, 63
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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 queen stands on, and Y the number of a square to which it can move. Then this sequence lists all possible values of YX.
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.)


LINKS



FORMULA



EXAMPLE

If a queen moves two squares to the left, e.g., from h8 to f8, this yields a difference Y  X = 2.
If a queen moves three squares up, e.g., from h1 to h4, this yields a difference Y  X = 3*8 = 24.


PROG

(PARI) Set(concat(Vec([1, 7, 8, 9]~*[7..7][^8])))


CROSSREFS



KEYWORD

sign,easy,fini,full


AUTHOR



STATUS

approved



