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A208533 Number of n-bead necklaces of n colors not allowing reversal, with no adjacent beads having the same color. 2
1, 1, 2, 24, 204, 2635, 39990, 720916, 14913192, 348684381, 9090909090, 261535848376, 8230246567620, 281241174889207, 10371206370593250, 410525522392242720, 17361641481138401520, 781282469565908953017, 37275544492386193492506, 1879498672877604463254424 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

a(n) = (1/n) * Sum_{d | n} totient(n/d) * ((n-1)*(-1)^d + (n-1)^d) for n > 1. - Andrew Howroyd, Mar 12 2017

EXAMPLE

All solutions for n=4:

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

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

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

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

..

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

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

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

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

MATHEMATICA

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

PROG

(PARI) a(n) = if (n==1, 1, (1/n) * sumdiv(n, d, eulerphi(n/d) * ((n-1)*(-1)^d + (n-1)^d))); \\ Michel Marcus, Nov 01 2017

CROSSREFS

Diagonal of A208535.

Sequence in context: A052780 A245019 A189769 * A174668 A302444 A121213

Adjacent sequences:  A208530 A208531 A208532 * A208534 A208535 A208536

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 27 2012

EXTENSIONS

a(14)-a(20) from Andrew Howroyd, Mar 12 2017

STATUS

approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)