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%I #14 Jan 25 2022 08:46:00
%S 4,8,18,126,380,4112,14310,184410,9272780,34669602,1857545300,
%T 26818405352,102282248574,1497215711538,84973644983780,
%U 4885261149611790,18900353608280300,1101298162244236182,16628051030379615882
%N Number of distinct necklaces with p beads of two possible colors, allowing turning over, p being a prime greater than 2.
%C For the general necklace problem, see A000029.
%D 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).
%F a(n) = (2^(p-1) - 1)/p + 2^{(p-1)/2} + 1 = A007663(n) + A061285(n) + 1.
%p 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
%Y Cf. A000029.
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Mar 07 2005
%E More terms from _James A. Sellers_, Apr 10 2005
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