A350191 - OEIS

A350191

Number of ways of placing maximum number of nonattacking rooks on a triangular board with edge-length n (not counting rotations and reflections as distinct).

%I #9 Dec 20 2021 01:40:57

%S 1,1,1,1,5,3,1,45,29,5,807,422,29,20022,8270,224,642162,211848,3012

%N Number of ways of placing maximum number of nonattacking rooks on a triangular board with edge-length n (not counting rotations and reflections as distinct).

%C a(n) = A350041(n) for n <> 10,13,16,19,...

%C Conjecture: a(3*n-2) = A309260(n). There is a nice analogy with A289893(3*n+1) = A002047(n).

%H Alain Brobecker, <a href="http://abrobecker.free.fr/text/NonAttackingRooks.pdf">Non Attacking Rooks on Hexhex and Triangular boards</a>

%H Vaclav Kotesovec, Example: <a href="/A350191/a350191.pdf">All non-identical positions for n = 10</a>, a(10) = 5

%Y Cf. A350041, A289893.

%K nonn,more,hard

%O 1,5

%A _Vaclav Kotesovec_, Dec 19 2021