A309260 Number of ways of placing 2n-1 nonattacking rooks on a hexagonal board with edge-length n in Glinski's hexagonal chess, inequivalent up to rotations and reflections of the board.

1, 1, 1, 5, 29, 224, 3012, 55200, 1259794, 35488536, 1200819600

Offset: 1

Author

Sangeet Paul, Jul 19 2019

Keywords

• nonn
• more
• hard

Comments

A rook in Glinski's hexagonal chess can move to any cell along the perpendicular bisector of any of the 6 edges of the hexagonal cell it's on (analogous to a rook in orthodox chess which can move to any cell along the perpendicular bisector of any of the 4 edges of the square cell it's on).

Examples

			a(1) = 1
.
  o
.
a(2) = 1
.
   o .
  . . o
   o .
.
a(3) = 1
.
    o . .
   . . o .
  . . . . o
   o . . .
    . o .
.
a(4) = 5
.
     o . . .        o . . .        o . . .        . o . .        . o . .
    . . o . .      . . o . .      . . . o .      o . . . .      . . . . o
   . . . . o .    . . . . . o    . . . . . o    . . . . . o    o . . . . .
  . . . . . . o  . o . . . . .  . . o . . . .  . . . o . . .  . . . o . . .
   o . . . . .    . . . . . o    o . . . . .    . . . . . o    . . . . . o
    . o . . .      . . o . .      . . . . o      o . . . .      o . . . .
     . . o .        o . . .        . o . .        . o . .        . . o .
.
		

Links

• Alain Brobecker, Non Attacking Rooks on Hexhex and Triangular boards
• Chess variants, Glinski's Hexagonal Chess
• Vaclav Kotesovec, All inequivalent solutions for n = 2,3,4 and 5
• Wikipedia, Hexagonal chess - Gliński's hexagonal chess

Crossrefs

Cf. A000903, A002047, A003215, A309746, A309669.

Extensions

a(1)-a(7) confirmed by Vaclav Kotesovec, Aug 16 2019

a(8) from Alain Brobecker, Dec 10 2021

a(8) confirmed by Vaclav Kotesovec, Dec 12 2021

a(9) from Alain Brobecker, Dec 13 2021

a(9) confirmed by Vaclav Kotesovec, Dec 18 2021

a(10)-a(11) from Bert Dobbelaere, Oct 24 2022