A357000 - OEIS

%I #25 Jun 28 2023 07:49:47

%S 1,2,3,5,5,12,9,22,21,44,29,157,73,244,367,649,521,2624,1609,7385,

%T 8867,19400,16769,92529,67553,216274,277191,815557,662369,4500266,

%U 2311469

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

%C 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.

%C 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.

%H Milan Hladnik, Dragan Marušič, and Tomaž Pisanski, <a href="https://doi.org/10.1016/S0012-365X(01)00064-4">Cyclic Haar graphs</a>, Discrete Mathematics 244 (2002), 137-152.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HaarGraph.html">Haar Graph</a>

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

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

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

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

%K nonn,more

%O 1,2

%A _Pontus von Brömssen_, Sep 08 2022

%E a(30) from _Eric W. Weisstein_, Jun 27 2023

%E a(31) from _Eric W. Weisstein_, Jun 28 2023