A278827 Queen's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially, row by row.

-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

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 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..54.

Formula

Equal to A278825 union A278826 (Bishop's and Rook's moves).

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

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

Contains all of A278825, A278826, A278828 and A278829 as a subsequence.

Sequence in context: A090635 A278825 A086859 * A125638 A365400 A365397

Adjacent sequences: A278824 A278825 A278826 * A278828 A278829 A278830

Keyword

sign,easy,fini,full

Author

M. F. Hasler, Nov 28 2016

Status

approved