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A302918
Number of nonequivalent minimal total dominating sets in the n-cycle graph up to rotation.
2
0, 0, 1, 1, 1, 2, 1, 1, 2, 3, 2, 4, 3, 4, 6, 7, 7, 10, 11, 17, 19, 23, 28, 38, 46, 60, 75, 96, 120, 160, 197, 257, 327, 420, 539, 701, 892, 1155, 1488, 1928, 2479, 3220, 4148, 5381, 6961, 9030, 11687, 15183, 19673, 25563, 33174, 43128, 56010, 72864, 94719
OFFSET
1,6
LINKS
Eric Weisstein's World of Mathematics, Cycle Graph
Eric Weisstein's World of Mathematics, Total Dominating Set
FORMULA
a(n) = (1/n) * Sum_{d|n} phi(n/d) * A300738(d).
MATHEMATICA
A300738 = DifferenceRoot[Function[{f, n}, {f[n] + f[n+1] - f[n+3] - f[n+4] - f[n+5] - f[n+6] + f[n+9] == 0, f[1]==0, f[2]==0, f[3]==3, f[4]==4, f[5]==5, f[6]==9, f[7]==7, f[8]==4, f[9]==12}]];
a[n_] := (1/n) Sum[EulerPhi[n/d] A300738[d], {d, Divisors[n]}];
a /@ Range[1, 55] (* Jean-François Alcover, Sep 21 2019 *)
PROG
(PARI)
NecklaceT(v)={vector(#v, n, sumdiv(n, d, eulerphi(n/d)*v[d])/n)}
NecklaceT(concat([0, 0], Vec((3 + 4*x + 5*x^2 + 6*x^3 - 8*x^5 - 9*x^6)/((1 - x^2 - x^3)*(1 + x^2 - x^6)) + O(x^50))))
CROSSREFS
Cf. A300738.
Sequence in context: A330334 A087741 A054991 * A316149 A047071 A124287
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Apr 15 2018
STATUS
approved