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A104137 Number of distinct necklaces with p beads of two possible colors, allowing turning over, p being a prime greater than 2. 0
4, 8, 18, 126, 380, 4112, 14310, 184410, 9272780, 34669602, 1857545300, 26818405352, 102282248574, 1497215711538, 84973644983780, 4885261149611790, 18900353608280300, 1101298162244236182, 16628051030379615882 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the general necklace problem, see A000029.

REFERENCES

Martin Gardner, The Colossal Book of Mathematics, pp. 19, W. W. Norton & Co., NY 2001 (or, New Mathematical Diversions, pp. 243-4 MAA Washington DC 1995).

LINKS

Table of n, a(n) for n=1..19.

FORMULA

a(n) = (2^(p-1) - 1)/p + 2^{(p-1)/2} + 1 = A007663(n) + A061285(n) + 1.

MAPLE

for p from 2 to 30 do printf(`%d, `, (2^(ithprime(p)-1)-1)/ithprime(p) + 2^((ithprime(p)-1)/2) + 1) od: # James A. Sellers, Apr 10 2005

CROSSREFS

Cf. A000029.

Sequence in context: A075310 A075797 A351323 * A308563 A272110 A272542

Adjacent sequences: A104134 A104135 A104136 * A104138 A104139 A104140

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Mar 07 2005

EXTENSIONS

More terms from James A. Sellers, Apr 10 2005

STATUS

approved

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Last modified December 8 08:22 EST 2022. Contains 358693 sequences. (Running on oeis4.)