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

1,2

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

Table of n, a(n) for n=1..31.

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(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).

Crossrefs

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

Sequence in context: A156834 A376017 A079024 * A342421 A319631 A097453

Adjacent sequences: A356997 A356998 A356999 * A357001 A357002 A357003

Keyword

nonn,more

Author

Pontus von Brömssen, Sep 08 2022

Extensions

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

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

Status

approved