A357003 Number of Hamiltonian cycles in the cyclic Haar graph with index n.

0, 0, 1, 0, 1, 1, 6, 0, 1, 0, 6, 1, 6, 6, 72, 0, 1, 1, 8, 1, 8, 8, 156, 1, 8, 8, 156, 8, 156, 156, 1440, 0, 1, 0, 8, 0, 12, 12, 335, 0, 12, 0, 300, 12, 352, 300, 4800, 1, 8, 12, 335, 12, 300, 352, 4800, 8, 335, 300, 4800, 335, 4800, 4800, 43200, 0, 1, 1, 10, 1

Offset: 1

Author

Pontus von Brömssen, Sep 08 2022

Keywords

• nonn

Comments

a(n) > 0 for all odd n >= 3 (Hladnik, Marušič, and Pisanski, 2002).

Links

• Pontus von Brömssen, Table of n, a(n) for n = 1..2047
• Milan Hladnik, Dragan Marušič, and Tomaž Pisanski, Cyclic Haar graphs, Discrete Mathematics 244 (2002), 137-152.
• Eric Weisstein's World of Mathematics, Haar Graph.

Crossrefs

Cf. A010796, A291165, A357000, A357004.

Formula

a(2^k-1) = A010796(k-1) for k >= 2.

a(A291165(n)) = 0.

a(n) = a(A357004(n)).