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 A054629 Number of n-bead necklaces with 10 colors. 3
 1, 10, 55, 340, 2530, 20008, 166870, 1428580, 12501280, 111111340, 1000010044, 9090909100, 83333418520, 769230769240, 7142857857190, 66666666680272, 625000006251280, 5882352941176480, 55555555611222370, 526315789473684220 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..19. Eric Weisstein's World of Mathematics, Necklace. Index entries for sequences related to necklaces FORMULA a(n) = (1/n)*Sum_{d|n} phi(d)*10^(n/d) = A054617(n)/n, n > 0. G.f.: 1 - Sum_{n>=1} phi(n)*log(1 - 10*x^n)/n. - Herbert Kociemba, Nov 02 2016 a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} 10^gcd(n,k). - Ilya Gutkovskiy, Apr 17 2021 EXAMPLE G.f. = 1 + 10*x + 55*x^2 + 340*x^3 + 2530*x^4 + 20008*x^5 + 166870*x^6 + ... MAPLE with(combstruct):A:=[N, {N=Cycle(Union(Z\$10))}, unlabeled]: seq(count(A, size=n), n=0..19); # Zerinvary Lajos, Dec 05 2007 MATHEMATICA mx=40; CoefficientList[Series[1-Sum[EulerPhi[i] Log[1-10*x^i]/i, {i, 1, mx}], {x, 0, mx}], x] (* Herbert Kociemba, Nov 02 2016 *) k=10; Prepend[Table[DivisorSum[n, EulerPhi[#] k^(n/#) &]/n, {n, 1, 30}], 1] (* Robert A. Russell, Sep 21 2018 *) PROG (PARI) a(n)=if(n==0, 1, 1/n*sumdiv(n, d, eulerphi(d)*10^(n/d))); \\ Altug Alkan, Sep 21 2018 CROSSREFS Column 10 of A075195. Cf. A054617. Sequence in context: A316109 A188168 A199413 * A290359 A030114 A001557 Adjacent sequences: A054626 A054627 A054628 * A054630 A054631 A054632 KEYWORD nonn AUTHOR N. J. A. Sloane, Apr 16 2000 EXTENSIONS Edited by Christian G. Bower, Sep 07 2002 a(0) corrected by Herbert Kociemba, Nov 02 2016 STATUS approved

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Last modified April 14 07:36 EDT 2024. Contains 371655 sequences. (Running on oeis4.)