The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A208595 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A208595

Number of n-bead necklaces labeled with numbers -6..6 not allowing reversal, with sum zero.
(history; published version)

#12 by Susanna Cuyler at Wed Nov 01 12:25:29 EDT 2017

STATUS

proposed

approved

#11 by Jean-François Alcover at Wed Nov 01 04:14:37 EDT 2017

STATUS

editing

proposed

#10 by Jean-François Alcover at Wed Nov 01 04:14:32 EDT 2017

MATHEMATICA

comps[r_, m_, k_] := Sum[(-1)^i*Binomial[r - 1 - i*m, k - 1]*Binomial[k, i], {i, 0, Floor[(r - k)/m]}]; a[n_Integer, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] = a[n, 6]; Array[a, 20] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

STATUS

approved

editing

#9 by Jon E. Schoenfield at Sun Mar 12 22:53:52 EDT 2017

STATUS

editing

approved

#8 by Jon E. Schoenfield at Sun Mar 12 22:53:48 EDT 2017

NAME

Number of n-bead necklaces labelled labeled with numbers -6..6 not allowing reversal, with sum zero.

EXAMPLE

Some solutions for n=4:

STATUS

approved

editing

#7 by N. J. A. Sloane at Thu Mar 02 21:01:33 EST 2017

STATUS

proposed

approved

#6 by Andrew Howroyd at Thu Mar 02 20:33:39 EST 2017

STATUS

editing

proposed

#5 by Andrew Howroyd at Thu Mar 02 19:58:47 EST 2017

DATA

1, 7, 43, 371, 3431, 34153, 353333, 3770475, 41165305, 457714497, 5164908167, 58997692301, 680874861687, 7926902673655, 92986983743513, 1097999648804923, 13040634990748733, 155677447454317639, 1866995100779692627, 22482675584863229261

COMMENTS

Column 6 of A208597

LINKS

Andrew Howroyd, <a href="/A208595/b208595.txt">Table of n, a(n) for n = 1..100</a>

FORMULA

a(n) = (1/n) * Sum_{d | n} totient(n/d) * A201550(d). - Andrew Howroyd, Mar 02 2017

CROSSREFS

Column 6 of A208597.

AUTHOR

R. H. Hardin , Feb 29 2012

EXTENSIONS

a(15)-a(20) from Andrew Howroyd, Mar 02 2017

STATUS

approved

editing

#4 by Russ Cox at Sat Mar 31 12:37:24 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Feb 29 2012

Discussion

Sat Mar 31

12:37

OEIS Server: https://oeis.org/edit/global/875

#3 by Ron Hardin at Wed Feb 29 11:05:04 EST 2012

STATUS

editing

approved