A278824 Knight moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row.

-17, -15, -10, -6, 6, 10, 15, 17

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 knight stands on, and Y the number of a square to which it can jump. 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 two rows up and one to the left yields a difference Y - X = 2*8 - 1 = 15. Moving two squares to the right and one down yields a difference Y - X = 2 - 8 = -6.

Crossrefs

Cf. A278825 - A278828, A278829 (analog for Bishops, ..., Kings and Pawns)

Sequence in context: A357190 A195534 A128158 * A085095 A004506 A096181

Adjacent sequences: A278821 A278822 A278823 * A278825 A278826 A278827

Keyword

sign,fini,easy,full

Author

M. F. Hasler, Nov 28 2016

Status

approved