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 A056288 Number of primitive (period n) n-bead necklaces with exactly three different colored beads. 4
 0, 0, 2, 9, 30, 89, 258, 720, 2016, 5583, 15546, 43215, 120750, 338001, 950030, 2677770, 7573350, 21478632, 61088874, 174179133, 497812378, 1425832077, 4092087522, 11765778330, 33887517840, 97756266615, 282414622728, 816999371955, 2366509198350, 6862929885407 (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 Sum mu(d)*A056283(n/d) where d|n. MAPLE with(numtheory): b:= proc(n, k) option remember; `if`(n=0, 1, add(mobius(n/d)*k^d, d=divisors(n))/n) end: a:= n-> add(b(n, 3-j)*binomial(3, j)*(-1)^j, j=0..3): seq(a(n), n=1..30); # Alois P. Heinz, Jan 25 2015 MATHEMATICA b[n_, k_] := b[n, k] = If[n==0, 1, DivisorSum[n, MoebiusMu[n/#]*k^#&]/n]; a[n_] := Sum[b[n, 3 - j]*Binomial[3, j]*(-1)^j, {j, 0, 3}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jun 06 2018, after Alois P. Heinz *) CROSSREFS Cf. A027376. Column k=3 of A254040. Sequence in context: A177111 A290746 A268586 * A261174 A273652 A056283 Adjacent sequences: A056285 A056286 A056287 * A056289 A056290 A056291 KEYWORD nonn AUTHOR Marks R. Nester STATUS approved

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Last modified July 25 05:51 EDT 2024. Contains 374586 sequences. (Running on oeis4.)