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

Author

Alois P. Heinz, Apr 14 2024

Keywords

• nonn

Examples

			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 |
  +-------+ +-------+ +-------+ +-------+ +-------+ +-------+ .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1788
• Wikipedia, Wazir (chess)

Crossrefs

Row maxima of A371967.

Cf. A371978.

Programs

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);