A278825 Bishop's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially, row by row.

-63, -54, -49, -45, -42, -36, -35, -28, -27, -21, -18, -14, -9, -7, 7, 9, 14, 18, 21, 27, 28, 35, 36, 42, 45, 49, 54, 63

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 bishop 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 bishop moves two squares to the upper left, e.g., from c1 to a3, this yields a difference Y - X = 2*(-1+8) = 14.

Prog

(PARI) Set(concat(Vec([7, 9]~*[-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: A145585 A033383 A090635 * A086859 A278827 A125638

Adjacent sequences: A278822 A278823 A278824 * A278826 A278827 A278828

Keyword

sign,easy,fini,full

Author

M. F. Hasler, Nov 28 2016

Status

approved