

A049297


Number of nonisomorphic circulant digraphs (i.e., Cayley digraphs for the cyclic group) of order n.


12



1, 2, 3, 6, 6, 20, 14, 46, 51, 140, 108, 624, 352, 1400, 2172, 4262, 4116, 22040, 14602, 68016, 88376, 209936, 190746, 1062592, 839094, 2797000, 3728891, 11276704, 9587580, 67195520, 35792568
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OFFSET

1,2


COMMENTS

Terms may be computed by filtering potentially isomorphic graphs of A056391 through nauty. Terms computed in this way for a(25), a(27) agree with theoretical calculations by others.  Andrew Howroyd, Apr 23 2017


LINKS

Table of n, a(n) for n=1..31.
V. A. Liskovets, Some identities for enumerators of circulant graphs, arXiv:math/0104131 [math.CO], 2001.
V. A. Liskovets and R. Poeschel, On the enumeration of circulant graphs of primepower and squarefree orders.
R. Poeschel, Publications.
V. Gatt, On the Enumeration of Circulant Graphs of PrimePower Order: the case of p^3, arXiv:1703.06038 [math.CO], 2017.
Brendan McKay, Nauty home page.


FORMULA

There is an easy formula for prime orders. Formulae are also known for squarefree and primesquared orders.
From Andrew Howroyd, Apr 23 2017: (Start)
a(n) <= A056391(n).
a(n) = A056391(n) for squarefree n.
a(A000040(n)^2) = A038777(n).
(End)


PROG

(GAP)
LoadPackage("grape");
CirculantDigraphCount:= function(n) local g; # slow for n >= 10
g:=Graph( Group(()), [1..n], OnPoints, function(x, y) return (yx) mod n = 1; end, false);
return Length(GraphIsomorphismClassRepresentatives(List(Combinations([1..n]), s>DistanceGraph(g, s))));
end; # Andrew Howroyd, Apr 23 2017


CROSSREFS

Cf. A049287A049289, A056391, A038777.
Sequence in context: A102625 A117777 A223547 * A285664 A056391 A056430
Adjacent sequences: A049294 A049295 A049296 * A049298 A049299 A049300


KEYWORD

nonn,nice


AUTHOR

Valery A. Liskovets


EXTENSIONS

Further values for (twice) squarefree and (twice) primesquared orders can be found in the Liskovets reference.
a(14) corrected by Andrew Howroyd, Apr 23 2017
a(16)a(31) from Andrew Howroyd, Apr 23 2017


STATUS

approved



