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 A032239 Number of identity bracelets of n beads of 2 colors. 2
 2, 1, 0, 0, 0, 1, 2, 6, 14, 30, 62, 127, 252, 493, 968, 1860, 3600, 6902, 13286, 25446, 48914, 93775, 180314, 346420, 666996, 1284318, 2477328, 4781007, 9240012, 17870709, 34604066, 67058880, 130084990, 252545160, 490722342 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For n>2 also number of asymmetric bracelets with n beads of two colors. - Herbert Kociemba, Nov 29 2016 LINKS C. G. Bower, Transforms (2) FORMULA "DHK" (bracelet, identity, unlabeled) transform of 2, 0, 0, 0... From Herbert Kociemba, Nov 29 2016: (Start) More generally, gf(k) is the g.f. for the number of asymmetric bracelets with n beads of k colors. gf(k): Sum_{n>=1} mu(n)*( -log(1-k*x^n)/n - Sum_{i=0..2} binomial(k,i)x^(n*i)/(1-k*x^(2*n)) )/2 (End) MATHEMATICA m = 2; (* asymmetric bracelets of n beads of m colors *) Table[Sum[MoebiusMu[d] (m^(n/d)/n - If[OddQ[n/d], m^((n/d + 1)/2), ((m + 1) m^(n/(2 d))/2)]), {d, Divisors[n]}]/2, {n, 3, 20}] (* Robert A. Russell, Mar 18 2013 *) mx=40; gf[x_, k_]:=Sum[MoebiusMu[n]*(-Log[1-k*x^n]/n-Sum[Binomial[k, i]x^(n i), {i, 0, 2}]/(1-k x^(2n)))/2, {n, mx}]; ReplacePart[Rest[CoefficientList[Series[gf[x, 2], {x, 0, mx}], x]], {1->2, 2->1}] (* Herbert Kociemba, Nov 29 2016 *) CROSSREFS Sequence in context: A110174 A022909 A292136 * A057094 A284938 A186084 Adjacent sequences:  A032236 A032237 A032238 * A032240 A032241 A032242 KEYWORD nonn AUTHOR STATUS approved

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Last modified October 22 20:57 EDT 2018. Contains 316502 sequences. (Running on oeis4.)