A278829 Pawn's moves in chess: possible difference between origin and destination square when the squares are numbered sequentially row by row.

-16, -9, -8, -7, 7, 8, 9, 16

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 pawn 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 starting value used for numbering, for example, one could also use number = column + 8 * row, 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 row by row, i.e., moving up or down one square must yield a difference of +- 8, and moving left or right (which a pawn can't do) must give a difference of +- 1. (All directions mentioned here correspond to a standard vertical diagram with White starting at the bottom and Black starting on the top.)

The positive values correspond to white pawns moving upwards, the negative values to black pawns moving downwards.

Links

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

Example

If a white pawn moves one row up, e.g., from c2 to c3, this yields a difference Y - X = +8. If a black pawn takes a white piece to the lower right, this yields a difference Y - X = -8 +1 = -7.
The steps of +- 16 correspond to pawns moving two squares ahead, starting from their initial position on the 2nd row (from bottom for white, from top for black).

Crossrefs

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

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

Sequence in context: A183396 A070535 A070579 * A066905 A302683 A302518

Adjacent sequences: A278826 A278827 A278828 * A278830 A278831 A278832

Keyword

sign,easy,fini,full

Author

M. F. Hasler, Nov 28 2016

Status

approved