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

1,7

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.

Formula

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

a(A291165(n)) = 0.

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

Crossrefs

Cf. A010796, A291165, A357000, A357004.

Sequence in context: A293071 A084680 A051626 * A264808 A200229 A137785

Adjacent sequences: A357000 A357001 A357002 * A357004 A357005 A357006

Keyword

nonn

Author

Pontus von Brömssen, Sep 08 2022

Status

approved