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A208724 Number of 2n-bead necklaces labeled with numbers 1..5 not allowing reversal, with neighbors differing by exactly 1. 3
4, 7, 12, 25, 52, 131, 316, 835, 2196, 5935, 16108, 44369, 122644, 341803, 956636, 2690845, 7596484, 21524543, 61171660, 174342217, 498112276, 1426419859, 4093181692, 11767920119, 33891544420, 97764131647, 282429537948, 817028472961, 2366564736724, 6863038218843 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..100

FORMULA

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A198635(d) / 2. - Andrew Howroyd, Mar 18 2017

EXAMPLE

All solutions for n=3:

..4....1....3....2....1....2....3....1....2....3....1....2

..5....2....4....3....2....3....4....2....3....4....2....3

..4....1....3....2....3....4....3....3....2....5....1....4

..5....2....4....3....2....3....4....4....3....4....2....5

..4....3....3....2....3....4....5....3....4....5....1....4

..5....2....4....3....2....3....4....2....3....4....2....3

MATHEMATICA

a[n_] := (1/n)*DivisorSum[n, EulerPhi[n/#] * (2*3^# + 2) &] / 2;

Array[a, 30] (* Jean-Fran├žois Alcover, Oct 31 2017, after Andrew Howroyd *)

CROSSREFS

Column 5 of A208727.

Sequence in context: A322619 A299900 A215329 * A183336 A102953 A111157

Adjacent sequences:  A208721 A208722 A208723 * A208725 A208726 A208727

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2012

EXTENSIONS

a(15)-a(30) from Andrew Howroyd, Mar 18 2017

STATUS

approved

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Last modified June 22 10:56 EDT 2021. Contains 345375 sequences. (Running on oeis4.)