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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 (list; graph; refs; listen; history; text; internal format)



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


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 prime-power and squarefree orders.

R. Poeschel, Publications.

V. Gatt, On the Enumeration of Circulant Graphs of Prime-Power Order: the case of p^3, arXiv:1703.06038 [math.CO], 2017.

Brendan McKay, Nauty home page.


There is an easy formula for prime orders. Formulae are also known for squarefree and prime-squared 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).





CirculantDigraphCount:= function(n) local g; # slow for n >= 10

g:=Graph( Group(()), [1..n], OnPoints, function(x, y) return (y-x) mod n = 1; end, false);

return Length(GraphIsomorphismClassRepresentatives(List(Combinations([1..n]), s->DistanceGraph(g, s))));

end; # Andrew Howroyd, Apr 23 2017


Cf. A049287-A049289, A056391, A038777.

Sequence in context: A102625 A117777 A223547 * A285664 A056391 A056430

Adjacent sequences:  A049294 A049295 A049296 * A049298 A049299 A049300




Valery A. Liskovets


Further values for (twice) squarefree and (twice) prime-squared 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



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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)