A278213 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 bishops of the same color on an n X n board.

0, 0, 0, 1, 2, 1, 0, 0, 4, 6, 8, 8, 8, 8, 6, 4, 0, 0, 5, 10, 13, 16, 17, 18, 19, 20, 19, 18, 17, 16, 12, 8, 4, 0, 0, 8, 14, 20, 24, 28, 30, 32, 34, 35, 36, 38, 38, 38, 37, 36, 36, 32, 28, 24, 20, 16, 12, 8, 4, 0

Offset

1,5

Links

Christian Sievers, Table of n, a(n) for n = 1..1512 (board size up to 16 X 16)

Example

T(4, 3) = 13 with the following 3 bishops on a 4x4 board:
   +---+---+---+---+
  4|   |   | B |   |
   +---+---+---+---+
  3|   |   | B |   |
   +---+---+---+---+
  2|   |   | B |   |
   +---+---+---+---+
  1|   |   |   |   |
   +---+---+---+---+
     A   B   C   D
The bishop at C4 has three legal moves and the bishops at C3 and C2 have five legal 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 1  2  1  0
  3| 0 4  6  8  8  8  8  6  4  0
  4| 0 5 10 13 16 17 18 19 20 19 18 17 16 12  8  4  0

Prog

(Python) # (using PuLP library) see links section of A278214

Crossrefs

Cf. A278212.

Sequence in context: A274776 A274777 A136129 * A034093 A246187 A079508

Adjacent sequences: A278210 A278211 A278212 * A278214 A278215 A278216

Keyword

nonn,tabf

Author

Peter Kagey, Nov 16 2016

Extensions

Definition corrected by Christian Sievers, Jun 11 2023

Status

approved