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A208775
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Number of n-bead necklaces labeled with numbers 1..6 not allowing reversal, with no adjacent beads differing by more than 1.
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3
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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PROG
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(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)) )
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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