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 A056290 Number of primitive (period n) n-bead necklaces with exactly five different colored beads. 4
 0, 0, 0, 0, 24, 300, 2400, 15750, 92680, 510288, 2691600, 13793850, 69309240, 343499100, 1686135352, 8221421250, 39901776360, 193053923860, 932142850800, 4495236287850, 21664357532920, 104388118174500, 503044634004000, 2425003910574000, 11696087875731600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 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)*A056285(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, 5-j)*binomial(5, j)*(-1)^j, j=0..5): 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, 5 - j]*Binomial[5, j]*(-1)^j, {j, 0, 5}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Jun 06 2018, after Alois P. Heinz *) CROSSREFS Cf. A001692. Column k=5 of A254040. Sequence in context: A162366 A153782 A073990 * A056285 A162686 A010976 Adjacent sequences:  A056287 A056288 A056289 * A056291 A056292 A056293 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 11 15:03 EST 2018. Contains 318049 sequences. (Running on oeis4.)