A278828 King's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row.

-9, -8, -7, -1, 1, 7, 8, 9

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 king 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 independent of the precise numbering scheme, provided that the numbers of the four possible neighbors of a square differ by +- 1 in one direction and +- 8 in the other direction. For example, one could also use number = row + 8 * column, where row and column range from 1 to 8, or from 0 to 7.

Links

Table of n, a(n) for n=1..8.

Example

Moving one row up yields a difference Y - X = +8. Moving one square diagonally down and right yields a difference Y - X = +1 - 8 = -7.

Crossrefs

Cf. A278824 - A278827, A278829 (analog for Knights, ..., Queens and Pawns).

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

Sequence in context: A094145 A002388 A248080 * A334448 A011116 A106334

Adjacent sequences: A278825 A278826 A278827 * A278829 A278830 A278831

Keyword

sign,fini,full,easy

Author

M. F. Hasler, Nov 28 2016

Status

approved