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A278214 Triangle read by rows: T(n, k) with 0 <= k <= n^2 is the maximum number of non-attacking moves that can be made by k queens on an n X n board. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..60.

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

CROSSREFS

Cf. A275815, A278213, A278215.

Sequence in context: A218610 A260958 A260965 * A072681 A244042 A318840

Adjacent sequences:  A278211 A278212 A278213 * A278215 A278216 A278217

KEYWORD

nonn,tabf,more

AUTHOR

Peter Kagey, Nov 16 2016

STATUS

approved

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Last modified June 5 01:27 EDT 2020. Contains 334828 sequences. (Running on oeis4.)