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%I #48 Oct 24 2022 15:13:07
%S 1,1,1,5,29,224,3012,55200,1259794,35488536,1200819600
%N 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.
%C 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).
%H Alain Brobecker, <a href="http://abrobecker.free.fr/text/NonAttackingRooks.pdf">Non Attacking Rooks on Hexhex and Triangular boards</a>
%H Chess variants, <a href="https://www.chessvariants.com/hexagonal.dir/hexagonal.html">Glinski's Hexagonal Chess</a>
%H Vaclav Kotesovec, <a href="/A309260/a309260.jpg">All inequivalent solutions for n = 2,3,4 and 5</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hexagonal_chess#Gli%C5%84ski's_hexagonal_chess">Hexagonal chess - Gliński's hexagonal chess</a>
%e a(1) = 1
%e .
%e o
%e .
%e a(2) = 1
%e .
%e o .
%e . . o
%e o .
%e .
%e a(3) = 1
%e .
%e o . .
%e . . o .
%e . . . . o
%e o . . .
%e . o .
%e .
%e a(4) = 5
%e .
%e o . . . o . . . o . . . . o . . . o . .
%e . . o . . . . o . . . . . o . o . . . . . . . . o
%e . . . . o . . . . . . o . . . . . o . . . . . o o . . . . .
%e . . . . . . o . o . . . . . . . o . . . . . . . o . . . . . . o . . .
%e o . . . . . . . . . . o o . . . . . . . . . . o . . . . . o
%e . o . . . . . o . . . . . . o o . . . . o . . . .
%e . . o . o . . . . o . . . o . . . . o .
%e .
%Y Cf. A000903, A002047, A003215, A309746, A309669.
%K nonn,more,hard
%O 1,4
%A _Sangeet Paul_, Jul 19 2019
%E a(1)-a(7) confirmed by _Vaclav Kotesovec_, Aug 16 2019
%E a(8) from _Alain Brobecker_, Dec 10 2021
%E a(8) confirmed by _Vaclav Kotesovec_, Dec 12 2021
%E a(9) from _Alain Brobecker_, Dec 13 2021
%E a(9) confirmed by _Vaclav Kotesovec_, Dec 18 2021
%E a(10)-a(11) from _Bert Dobbelaere_, Oct 24 2022
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