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A115120 Number of imprimitive (periodic) 2n-bead black-white reversible necklaces with n black beads. 0
0, 0, 1, 1, 2, 1, 4, 1, 8, 3, 17, 1, 56, 1, 134, 18, 440, 1, 1434, 1, 4758, 135, 16160, 1, 57254, 16, 200475, 1387, 718152, 1, 2591800, 1, 9398520, 16161, 34324175, 148, 126125330, 1, 465093572, 200476, 1723176740, 1, 6408642359, 1, 23910576236, 2588402, 89494164974, 1, 335923316982, 133, 1264107421202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(p)=1 for prime p.

LINKS

Table of n, a(n) for n=0..50.

FORMULA

a(n) = A005648(n) - A045628(n).

MATHEMATICA

A005648[0] = 1; A005648[n_] := (1/2)(Binomial[2 Quotient[n, 2], Quotient[n, 2]] + DivisorSum[n, EulerPhi[#] Binomial[2n/#, n/#] &]/(2n));

A045628[n_] := If[n == 0, 1, Sum[MoebiusMu[n/d] (2n Binomial[2 Quotient[d, 2], Quotient[d, 2]] + Binomial[2d, d]), {d, Divisors[n]}]/(4n)];

a[n_] := A005648[n] - A045628[n];

Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Aug 28 2019 *)

CROSSREFS

Sequence in context: A248058 A072345 A200583 * A147373 A147441 A146269

Adjacent sequences:  A115117 A115118 A115119 * A115121 A115122 A115123

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Jan 17 2006

EXTENSIONS

More terms from Jean-François Alcover, Aug 28 2019

STATUS

approved

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Last modified May 28 17:28 EDT 2020. Contains 334684 sequences. (Running on oeis4.)