login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208542 Number of n-bead necklaces of 6 colors allowing reversal, with no adjacent beads having the same color. 2
6, 15, 20, 120, 312, 1505, 5580, 25395, 108520, 493131, 2219460, 10196680, 46950120, 218102685, 1017252828, 4768969770, 22439395680, 105966797755, 501933850740, 2384200683816, 11353265675240, 54186115056825, 259150629458220, 1241763804134805 (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(2n+1) = A106368(2n+1)/2 for n > 0, a(2n) = (A106368(2n) + 3*5^n)/2. - Andrew Howroyd, Mar 12 2017

EXAMPLE

All solutions for n=3:

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

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

..6....5....5....6....6....6....5....6....5....4....5....4....6....5....6....3

..

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

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

..6....4....6....6

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, 6]; Array[a, 24] (* Jean-Fran├žois Alcover, Nov 01 2017, after Andrew Howroyd *)

CROSSREFS

Column 6 of A208544.

Sequence in context: A196394 A162693 A056901 * A012412 A009092 A330205

Adjacent sequences:  A208539 A208540 A208541 * A208543 A208544 A208545

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 27 2012

EXTENSIONS

a(19)-a(24) from Andrew Howroyd, Mar 12 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)