A104137 Number of distinct necklaces with p beads of two possible colors, allowing turning over, p being a prime greater than 2.

4, 8, 18, 126, 380, 4112, 14310, 184410, 9272780, 34669602, 1857545300, 26818405352, 102282248574, 1497215711538, 84973644983780, 4885261149611790, 18900353608280300, 1101298162244236182, 16628051030379615882

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