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 A208775 Number of n-bead necklaces labeled with numbers 1..6 not allowing reversal, with no adjacent beads differing by more than 1. 3
 6, 11, 16, 30, 52, 117, 242, 577, 1360, 3347, 8278, 20978, 53346, 137422, 355978, 928731, 2434580, 6414014, 16961468, 45017417, 119840582, 319916277, 856089572, 2295950281, 6169664562, 16608996492, 44785220118, 120942143132, 327053057574, 885545659155, 2400570958904, 6514679288762, 17697582670400, 48122529680805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..100 Arnold Knopfmacher, Toufik Mansour, Augustine Munagi, Helmut Prodinger, Smooth words and Chebyshev polynomials, arXiv:0809.0551 [math.CO], 2008. FORMULA a(n) = (1/n) * Sum_{d | n} totient(n/d) * A124699(n). - Andrew Howroyd, Mar 18 2017 EXAMPLE All solutions for n=3: ..5....1....1....3....5....5....1....2....2....3....3....6....2....4....4....4 ..5....1....2....3....6....5....1....3....2....3....4....6....2....4....5....4 ..5....2....2....4....6....6....1....3....2....3....4....6....3....4....5....5 MATHEMATICA sn[n_, k_] := 1/n*Sum[ Sum[ EulerPhi[j]*(1 + 2*Cos[i*Pi/(k + 1)])^(n/j), {j, Divisors[n]}], {i, 1, k}]; Table[sn[n, 6], {n, 1, 34}] // FullSimplify (* Jean-François Alcover, Oct 31 2017, after Joerg Arndt *) PROG (PARI) /* from the Knopfmacher et al. reference */ default(realprecision, 99); /* using floats */ sn(n, k)=1/n*sum(i=1, k, sumdiv(n, j, eulerphi(j)*(1+2*cos(i*Pi/(k+1)))^(n/j))); vector(66, n, round(sn(n, 6)) ) /* Joerg Arndt, Aug 09 2012 */ CROSSREFS Column 6 of A208777. Sequence in context: A276038 A191158 A208719 * A242916 A256429 A024730 Adjacent sequences:  A208772 A208773 A208774 * A208776 A208777 A208778 KEYWORD nonn AUTHOR R. H. Hardin, Mar 01 2012 STATUS approved

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