The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A278828 King's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row. 5

%I #13 Nov 30 2016 01:16:28

%S -9,-8,-7,-1,1,7,8,9

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

%C 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.

%C 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.

%e 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.

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

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

%K sign,fini,full,easy

%O 1,1

%A _M. F. Hasler_, Nov 28 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 20 14:08 EDT 2024. Contains 372717 sequences. (Running on oeis4.)