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 A081721 Number of bracelets of n beads in up to n colors. 18
 1, 3, 10, 55, 377, 4291, 60028, 1058058, 21552969, 500280022, 12969598086, 371514016094, 11649073935505, 396857785692525, 14596464294191704, 576460770691256356, 24330595997127372497, 1092955780817066765469, 52063675152021153895330, 2621440000054016000176044 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS T(n,n), T given in A081720. From Olivier Gérard, Aug 01 2016: (Start) Number of classes of functions of [n] to [n] under rotation and reversal. . Classes can be of size between 1 and 2n depending on divisibility properties of n. . n   1   2   3   4    5         n     2n ---------------------------------------- 1   1 2   2   1 3   3   0   6                         1 4   4   6   0                 30     15 5   5   0   0                120    252 6   6  15  30                725   3515 7   7   0   0               2394  57627 . (End) LINKS Alois P. Heinz, Table of n, a(n) for n = 1..200 FORMULA a(n) ~ n^(n-1) / 2. - Vaclav Kotesovec, Mar 18 2017 MATHEMATICA Table[CycleIndex[DihedralGroup[n], s]/.Table[s[i]->n, {i, 1, n}], {n, 1, 20}] (* Geoffrey Critzer, Jun 18 2013 *) t[n_, k_] := (For[t1 = 0; d = 1, d <= n, d++, If[Mod[n, d] == 0, t1 = t1 + EulerPhi[d]*k^(n/d)]]; If[EvenQ[n], (t1 + (n/2)*(1 + k)*k^(n/2))/(2*n), (t1 + n*k^((n + 1)/2))/(2*n)]); a[n_] := t[n, n]; Array[a, 20] (* Jean-François Alcover, Nov 02 2017, after Maple code for A081720 *) CROSSREFS Cf. A000312 All endofunctions Cf. A000169 Classes under translation mod n Cf. A001700 Classes under sort Cf. A056665 Classes under rotation Cf. A168658 Classes under complement to n+1 Cf. A130293 Classes under translation and rotation Cf. A275549 Classes under reversal Cf. A275550 Classes under reversal and complement Cf. A275551 Classes under translation and reversal Cf. A275552 Classes under translation and complement Cf. A275553 Classes under translation, complement and reversal Cf. A275554 Classes under translation, rotation and complement Cf. A275555 Classes under translation, rotation and reversal Cf. A275556 Classes under translation, rotation, complement and reversal Cf. A275557 Classes under rotation and complement Cf. A275558 Classes under rotation, complement and reversal Row sums of partition array A213941. Sequence in context: A208480 A034234 A284645 * A013009 A203416 A002218 Adjacent sequences:  A081718 A081719 A081720 * A081722 A081723 A081724 KEYWORD nonn AUTHOR N. J. A. Sloane, based on information supplied by Gary W. Adamson, Apr 05 2003 EXTENSIONS Name changed by Olivier Gérard, Aug 05 2016 Name revised by Álvar Ibeas, Apr 20 2018 STATUS approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)