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

Author

Lekraj Beedassy, Mar 07 2005

Keywords

• nonn

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).

Crossrefs

Cf. A000029.

Programs

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 Sellers, Apr 10 2005

Formula

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

Extensions

More terms from James Sellers, Apr 10 2005