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A032275 Number of bracelets (turn over necklaces) of n beads of 4 colors. 8
4, 10, 20, 55, 136, 430, 1300, 4435, 15084, 53764, 192700, 704370, 2589304, 9608050, 35824240, 134301715, 505421344, 1909209550, 7234153420, 27489127708, 104717491064, 399827748310, 1529763696820 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..23.

C. G. Bower, Transforms (2)

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

Index entries for sequences related to bracelets

FORMULA

"DIK" (bracelet, indistinct, unlabeled) transform of 4, 0, 0, 0...

G.f.: (1 - Sum_{n>=1} phi(n)*log(1 - 4*x^n)/n + (1+4*x+6*x^2)/(1-4*x^2))/2. - Herbert Kociemba, Nov 02 2016

MATHEMATICA

mx=40; CoefficientList[Series[(1-Sum[ EulerPhi[n]*Log[1-4*x^n]/n, {n, mx}]+(1+4 x+6 x^2)/(1-4 x^2))/2, {x, 0, mx}], x] (* Herbert Kociemba, Nov 02 2016 *)

CROSSREFS

Cf. a(n) = A081720(n,4), n>=4. [From Wolfdieter Lang, Jun 03 2012]

Sequence in context: A237626 A020149 A056412 * A220828 A015220 A047199

Adjacent sequences:  A032272 A032273 A032274 * A032276 A032277 A032278

KEYWORD

nonn

AUTHOR

Christian G. Bower

STATUS

approved

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Last modified February 23 22:17 EST 2018. Contains 299595 sequences. (Running on oeis4.)