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A007148
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Number of self-complementary 2-colored bracelets (turn over necklaces) with 2n beads.
(Formerly M0774)
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4
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1, 2, 3, 6, 10, 20, 37, 74, 143, 284, 559, 1114, 2206, 4394, 8740, 17418, 34696, 69194, 137971, 275280, 549258, 1096286, 2188333, 4369162, 8724154, 17422652, 34797199, 69505908, 138845926, 277383872, 554189329, 1107297290, 2212558942
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| E. M. Palmer and R. W. Robinson, Enumeration of self-dual configurations Pacific J. Math., 110 (1984), 203-221.
F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.
Index entries for sequences related to bracelets
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FORMULA
| a(n)= (1/2) *(A000079(n-1)+A000013(n)).
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MATHEMATICA
| a[n_] := (1/2)*(2^(n-1) + Total[ EulerPhi[2*#]*2^(n/#) & /@ Divisors[n]]/(2*n)); Table[ a[n], {n, 1, 33}] (* From Jean-François Alcover, Oct 25 2011 *)
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PROG
| (PARI) a(n)= (1/2) *(2^(n-1)+sumdiv(n, k, eulerphi(2*k)*2^(n/k))/(2*n))
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CROSSREFS
| Cf. A000013, A000079, A007147.
Sequence in context: A164047 A158291 A045690 * A093371 A003214 A123423
Adjacent sequences: A007145 A007146 A007147 * A007149 A007150 A007151
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Description corrected by Christian G. Bower (bowerc(AT)usa.net). More terms from Michael Somos
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