A278826 Rook's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially, row by row.

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

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 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.

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

Table of n, a(n) for n=1..28.

Example

If a rook moves two squares to the left, e.g., from h8 to f8, this yields a difference Y - X = -2.
If a rook 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, 8]~*[-7..7][^8])))

Crossrefs

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

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

Sequence in context: A300449 A224343 A369234 * A259537 A359604 A292092

Adjacent sequences: A278823 A278824 A278825 * A278827 A278828 A278829

Keyword

sign,easy,fini,full

Author

M. F. Hasler, Nov 28 2016

Status

approved