A371979 Number of ways of placing k non-attacking wazirs on a 3 X n board, where k is chosen so as to maximize this number.

1, 3, 8, 24, 84, 276, 880, 3063, 10692, 36257, 121580, 436847, 1530534, 5259906, 18389910, 65748491, 230935493, 799429185, 2860613606, 10203350814, 35899202776, 125660232367, 453360413253, 1614905346286, 5688690345179, 20241845359246, 72805688610204

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1788

Wikipedia, Wazir (chess)

Example

a(3) = 24 = A371967(3,2):
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  | W . W | | W . . | | W . . | | W . . | | W . . | | W . . |
  | . . . | | . W . | | . . W | | . . . | | . . . | | . . . |
  | . . . | | . . . | | . . . | | W . . | | . W . | | . . W |
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  | . W . | | . W . | | . W . | | . W . | | . W . | | . . W |
  | W . . | | . . W | | . . . | | . . . | | . . . | | W . . |
  | . . . | | . . . | | W . . | | . W . | | . . W | | . . . |
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  | . . W | | . . W | | . . W | | . . W | | . . . | | . . . |
  | . W . | | . . . | | . . . | | . . . | | W . W | | W . . |
  | . . . | | W . . | | . W . | | . . W | | . . . | | . W . |
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+
  | . . . | | . . . | | . . . | | . . . | | . . . | | . . . |
  | W . . | | . W . | | . W . | | . . W | | . . W | | . . . |
  | . . W | | W . . | | . . W | | W . . | | . W . | | W . W |
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+ .

Maple

b:= proc(n, l) option remember; `if`(n=0, 1,
      add(`if`(Bits[And](j, l)>0, 0, expand(b(n-1, j)*
      x^add(i, i=Bits[Split](j)))), j=[0, 1, 2, 4, 5]))
    end:
a:= n-> max(coeffs(b(n, 0))):
seq(a(n), n=0..30);

Crossrefs

Row maxima of A371967.

Cf. A371978.

Sequence in context: A088966 A242985 A148787 * A125655 A134165 A071016

Adjacent sequences: A371976 A371977 A371978 * A371982 A371983 A371985

Keyword

nonn

Author

Alois P. Heinz, Apr 14 2024

Status

approved