A278214 Triangle read by rows: T(n, k) with 0 <= k <= n^2 is the maximum number of possible moves that can be made by k queens of the same color on an n X n board.

0, 0, 0, 3, 4, 3, 0, 0, 8, 12, 16, 17, 16, 14, 12, 8, 0, 0, 11, 20, 29, 36, 38, 40, 40, 40, 38, 36, 34, 32, 24, 16, 8, 0, 0, 16, 28, 40, 52, 64, 67, 70, 73, 74, 75, 76, 74, 72, 72, 72, 72, 64, 56, 48, 40, 32, 24, 16, 8, 0

Offset

1,4

Links

Christian Sievers, Table of n, a(n) for n = 1..395 (board size up to 10 X 10)

Christian Sievers, Python/PuLP program for specified or arbitrary number of pieces (queens, rooks resp. bishops)

Formula

T(n, 0) = 0.

T(n, n^2 - k) = 8*k for n >= 2 and 0 <= k <= (n - 2)^2.

Example

T(4, 3) = 29 with the following 3 queens on a 4 X 4 board:
   +---+---+---+---+
  4|   |   | Q |   |
   +---+---+---+---+
  3|   |   |   |   |
   +---+---+---+---+
  2|   | Q |   |   |
   +---+---+---+---+
  1|   |   |   | Q |
   +---+---+---+---+
     A   B   C   D
The queen on B2 has 11 moves, and the queens on C4 and D1 have 9 moves each.
Table begins:
n\k| 0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16
---+--------------------------------------------------
  1| 0  0
  2| 0  3  4  3  0
  3| 0  8 12 16 17 16 14 12  8  0
  4| 0 11 20 29 36 38 40 40 40 38 36 34 32 24 16  8  0

Prog

(Python) # (using PuLP library) see links section

Crossrefs

Cf. A275815, A278213, A278215.

Sequence in context: A346058 A260958 A260965 * A359601 A072681 A244042

Adjacent sequences: A278211 A278212 A278213 * A278215 A278216 A278217

Keyword

nonn,tabf

Author

Peter Kagey, Nov 16 2016

Extensions

Definition corrected by Christian Sievers, Jun 11 2023

Status

approved