A362601 Domination number for pawns' graph P(n).

1, 2, 5, 8, 12, 16, 23, 28, 33, 44, 49, 56, 70, 78, 85, 104, 111, 120, 141, 152, 161, 188, 197, 208, 237, 250, 261, 296, 307, 320, 357, 372, 385, 428, 441, 456, 501, 518, 533, 584

Offset

1,2

Comments

Minimum number of white pawns needed to occupy or attack all squares of an n X n chessboard.

Solutions for boards of sizes 1 to 8, 10, 14, 15 from Rodolfo Kurchan.

Solutions for boards of sizes 9, 11, 12, 14 to 18, 20 to 24 from Michael Steinau.

Solution for boards of size 13 and 25 to 40 from M. Achterberg.

Links

Table of n, a(n) for n=1..40.

M. Achterberg, Illustration for a(13) = 70.

Rodolfo Kurchan, Board domination problem, Chess Puzzle Fun 6, April 2023.

Example

a(8) = 28 white pawns occupying or attacking all squares of a standard chessboard:
  . . . . . . . .
  . P P P P P P .
  . P . . . . P .
  . P . P P . P .
  . P . . . . P .
  . P . P P . P .
  . P . . . . P .
  P P P P P P P P

Crossrefs

Cf. A075458.

Sequence in context: A219657 A213707 A229154 * A174605 A108577 A272719

Adjacent sequences: A362598 A362599 A362600 * A362602 A362603 A362604

Keyword

nonn,more

Author

Rodolfo Kurchan, Jun 18 2023

Status

approved