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A208538 Number of n-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color. 2
1, 1, 1, 21, 102, 1505, 19995, 365260, 7456596, 174489813, 4545454545, 130773238871, 4115123283810, 140620807064413, 5185603185296625, 205262771447683860, 8680820740569200760, 390641235316599920745, 18637772246193096746253, 939749336469457562916217 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..80

FORMULA

a(2n+1) = A208533(2n+1)/2 for n > 0, a(2n) = (A208533(2n) + n*(2n-1)^n)/2. - Andrew Howroyd, Mar 12 2017

EXAMPLE

All solutions for n=4:

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

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

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

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

..

..1....1....2....1....1

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

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

..4....4....3....4....4

MATHEMATICA

T[n_, k_] := If[n == 1, k, (DivisorSum[n, EulerPhi[n/#]*(k - 1)^# &]/n + If[OddQ[n], 1 - k, k*(k - 1)^(n/2)/2])/2]; a[n_] = T[n, n]; Array[a, 20] (* Jean-Fran├žois Alcover, Nov 01 2017, after Andrew Howroyd *)

CROSSREFS

Diagonal of A208544.

Sequence in context: A044272 A044653 A076454 * A303681 A304132 A304220

Adjacent sequences:  A208535 A208536 A208537 * A208539 A208540 A208541

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 27 2012

EXTENSIONS

a(12)-a(20) from Andrew Howroyd, Mar 12 2017

STATUS

approved

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Last modified February 23 09:04 EST 2019. Contains 320420 sequences. (Running on oeis4.)