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Search: id:A104137
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| A104137 |
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Number of distinct necklaces with p beads of two possible colors, allowing turning over, p being a prime greater than 2. |
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+0
1
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| 4, 8, 18, 126, 380, 4112, 14310, 184410, 9272780, 34669602, 1857545300, 26818405352, 102282248574, 1497215711538, 84973644983780, 4885261149611790, 18900353608280300, 1101298162244236182, 16628051030379615882
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For the general necklace problem, see A000029.
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REFERENCES
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M.Gardner, The Colossal Book of Mathematics, pp. 19 W.W.Norton & Co. NY 2001(or, New Mathematical Diversions, pp. 243-4 MAA Wasington DC 1995).
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FORMULA
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a(n) = (2^(p-1) - 1)/p + 2^{(p-1)/2} + 1 = A007663(n) + A061285(n) + 1.
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MAPLE
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for p from 2 to 30 do printf(`%d, `, (2^(ithprime(p)-1)-1)/ithprime(p) + 2^((ithprime(p)-1)/2) + 1) od: (Sellers)
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CROSSREFS
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Cf. A000029.
Sequence in context: A080287 A075310 A075797 this_sequence A162362 A130887 A049933
Adjacent sequences: A104134 A104135 A104136 this_sequence A104138 A104139 A104140
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Mar 07 2005
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 10 2005
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