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 A056289 Number of primitive (period n) n-bead necklaces with exactly four different colored beads. 5
 0, 0, 0, 6, 48, 260, 1200, 5100, 20720, 81828, 318000, 1222870, 4675440, 17813820, 67769504, 257695800, 980240880, 3731732200, 14222737200, 54278498154, 207438936800, 793940157900, 3043140078000, 11681056021300, 44900438149248, 172824327151140, 666070256468960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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) = Sum_{d|n} mu(d)*A056284(n/d). 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, 4-j)*binomial(4, j)*(-1)^j, j=0..4): 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, 4-j]*Binomial[4, j]*(-1)^j, {j, 0, 4}]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 20 2017, after Alois P. Heinz *) CROSSREFS Cf. A027377. Column k=4 of A254040. Sequence in context: A260344 A262354 A052771 * A056284 A246587 A229504 Adjacent sequences:  A056286 A056287 A056288 * A056290 A056291 A056292 KEYWORD nonn AUTHOR Marks R. Nester (nesterm(AT)dpi.qld.gov.au) STATUS approved

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