

A056283


Number of nbead necklaces with exactly three different colored beads.


7



0, 0, 2, 9, 30, 91, 258, 729, 2018, 5613, 15546, 43315, 120750, 338259, 950062, 2678499, 7573350, 21480739, 61088874, 174184755, 497812638, 1425847623, 4092087522, 11765822365, 33887517870, 97756387365, 282414624746, 816999710223, 2366509198350, 6862930841141
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Turning over the necklace is not allowed.


REFERENCES

M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A001867(n)  3*A000031(n) + 3.
From Robert A. Russell, Sep 26 2018: (Start)
a(n) = (k!/n) Sum_{dn} phi(d) S2(n/d,k), where k=3 is the number of colors and S2 is the Stirling subset number A008277.
G.f.: Sum_{d>0} (phi(d)/d) * Sum_{j} (1)^(kj) * C(k,j) * log(1j x^d), where k=3 is the number of colors. (End)


EXAMPLE

For n=3, the two necklaces are ABC and ACB.


MATHEMATICA

k=3; Table[k!DivisorSum[n, EulerPhi[#]StirlingS2[n/#, k]&]/n, {n, 1, 30}] (* Robert A. Russell, Sep 26 2018 *)


CROSSREFS

Cf. A000031, A001867, A052823.
Column k=3 of A087854.
Sequence in context: A056288 A261174 A273652 * A192518 A277241 A201164
Adjacent sequences: A056280 A056281 A056282 * A056284 A056285 A056286


KEYWORD

nonn


AUTHOR

Marks R. Nester


STATUS

approved



