A357000 Number of non-isomorphic cyclic Haar graphs on 2*n nodes.

1, 2, 3, 5, 5, 12, 9, 22, 21, 44, 29, 157, 73, 244, 367, 649, 521, 2624, 1609, 7385, 8867, 19400, 16769, 92529, 67553, 216274, 277191, 815557, 662369, 4500266, 2311469

Offset: 1

Author

Pontus von Brömssen, Sep 08 2022

Keywords

• nonn
• more

Comments

The first value of n for which a(n) < A002729(n) - 1 is n = 8. This is because the first counterexample to the bicirculant analog to Ádám's conjecture occurs for n = 8. In the terminology of Hladnik, Marušič, and Pisanski, the smallest integer pair (i,j) such that i and j are Haar equivalent (i.e., the cyclic Haar graphs with indices i and j are isomorphic) but not cyclically equivalent (see A357005) is (141,147). See also A357001 and A357002.

Terms a(1)-a(29) were found by generating the cyclic Haar graphs with indices in A333764, and filtering out isomorphic graphs using Brendan McKay's software nauty.

Links

• 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. A002729, A008965, A049287, A091696, A137706, A291166, A333764, A339502, A357001, A357002, A357003, A357004, A357005, A357006.

Formula

a(n) is the number of terms k of A137706 in the interval 2^(n-1) <= k < 2^n.

a(n) is the number of fixed points k of A357004 in the interval 2^(n-1) <= k < 2^n.

a(n) <= A002729(n)-1 <= A091696(n) <= A008965(n).

Extensions

a(30) from Eric W. Weisstein, Jun 27 2023

a(31) from Eric W. Weisstein, Jun 28 2023