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

1,4

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).

Links

Table of n, a(n) for n=1..11.

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

Example

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 .
.

Crossrefs

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

Sequence in context: A356336 A352294 A182018 * A087662 A113012 A000354

Adjacent sequences: A309257 A309258 A309259 * A309261 A309262 A309263

Keyword

nonn,more,hard

Author

Sangeet Paul, Jul 19 2019

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

Status

approved