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!)
A208774 Number of n-bead necklaces labeled with numbers 1..5 not allowing reversal, with no adjacent beads differing by more than 1. 4
5, 9, 13, 24, 41, 91, 185, 435, 1009, 2445, 5945, 14813, 36977, 93465, 237313, 606465, 1556033, 4010205, 10367897, 26891385, 69930457, 182302161, 476262761, 1246710303, 3269321393, 8587489185, 22590646417, 59511087087, 156973954865, 414552479249, 1096017973385, 2900753690865, 7684758676201, 20377462520193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Arnold Knopfmacher, Toufik Mansour, Augustine Munagi, Helmut Prodinger, Smooth words and Chebyshev polynomials, arXiv:0809.0551v1 [math.CO], 2008.

FORMULA

a(n) = Sum_{ d | n } A215337(d). - Joerg Arndt, Aug 13 2012

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A124698(n). - Andrew Howroyd, Mar 18 2017

EXAMPLE

All solutions for n=3:

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

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

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

MATHEMATICA

sn[n_, k_] := 1/n*Sum[DivisorSum[n, EulerPhi[#]*(1 + 2*Cos[i*Pi/(k + 1)])^(n/#)&], {i, 1, k}]; Table[sn[n, 5], {n, 1, 34}] // Simplify (* Jean-Fran├žois Alcover, Oct 31 2017, after Joerg Arndt *)

PROG

(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, 5)) )

/* Joerg Arndt, Aug 09 2012 */

CROSSREFS

Column 5 of A208777.

Cf. A215337 (cyclically smooth Lyndon words with 5 colors).

Sequence in context: A314797 A314798 A208718 * A271391 A151907 A151895

Adjacent sequences:  A208771 A208772 A208773 * A208775 A208776 A208777

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 01 2012

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 March 31 23:42 EDT 2020. Contains 333152 sequences. (Running on oeis4.)