The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A208590

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A208590

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

#13 by Susanna Cuyler at Wed Nov 01 12:24:49 EDT 2017

STATUS

proposed

approved

#12 by Jean-François Alcover at Wed Nov 01 03:49:03 EDT 2017

STATUS

editing

proposed

#11 by Jean-François Alcover at Wed Nov 01 03:48:56 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_, k_] := DivisorSum[n, EulerPhi[n/#] comps[#*(k + 1), 2 k + 1, #] &]/n; a[n_] := a[n, n]; Array[a, 18] (* Jean-François Alcover, Nov 01 2017, after Andrew Howroyd *)

STATUS

approved

editing

#10 by Jon E. Schoenfield at Sun Mar 12 22:55:59 EDT 2017

STATUS

editing

approved

#9 by Jon E. Schoenfield at Sun Mar 12 22:55:54 EDT 2017

NAME

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

EXAMPLE

All solutions for n=3:

STATUS

approved

editing

#8 by N. J. A. Sloane at Thu Mar 02 23:07:29 EST 2017

STATUS

proposed

approved

#7 by Andrew Howroyd at Thu Mar 02 21:10:09 EST 2017

STATUS

editing

proposed

#6 by Andrew Howroyd at Thu Mar 02 21:09:05 EST 2017

DATA

1, 3, 13, 125, 1761, 34153, 833253, 24627705, 855798877, 34223775091, 1549090700059, 78325577416281, 4376902102440375, 267933660979057571, 17834397187887850661, 1282662234529669344753, 99133711906097886767313, 8194555387462964814207631

COMMENTS

Diagonal of A208597

LINKS

Andrew Howroyd, <a href="/A208590/b208590.txt">Table of n, a(n) for n = 1..80</a>

CROSSREFS

Diagonal of A208597.

AUTHOR

R. H. Hardin , Feb 29 2012

EXTENSIONS

a(12)-a(18) from Andrew Howroyd, Mar 02 2017

STATUS

approved

editing

#5 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

#4 by Ron Hardin at Wed Feb 29 10:58:06 EST 2012

STATUS

editing

approved