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%I #27 Jul 26 2023 21:00:48
%S 0,0,0,1,2,4,9,15,30,54,101,181,344,624,1173,2183,4106,7702,14591,
%T 27585,52476,99868,190733,364711,699238,1342170,2581413,4971053,
%U 9587564,18512776,35792551,69273651,134219778,260301158
%N Number of black and white n-bead necklaces with at least 3 white beads (turning over is not allowed); also number of clockwise arrangements of reflex and non-reflex angles that can form an n-gon.
%C A reflex angle is an angle with measure greater than Pi or 180 degrees. Every polygon has at least three angles with measure less than Pi or 180 degrees.
%H Danny Rorabaugh, <a href="/A262232/b262232.txt">Table of n, a(n) for n = 0..500</a>
%H Danny Rorabaugh, <a href="/A262232/a262232_1.png">Polygon demonstration of a(6)=9</a>
%F a(n) = A000031(n) - 2 - floor(n/2), n>0.
%e Let 1's represent black beads and 0's represent white beads. For n=6, the a(6)=9 necklaces are 000000, 000001, 000011, 000101, 000111, 001001, 001011, 001101, 010101. Note that 001011 and 001101 would be equivalent if "turning over" were allowed.
%o (Sage) [sum([Necklaces([n-k,k]).cardinality() for k in range(n-2)]) for n in range(34)]
%Y Cf. A000031, A227910.
%K nonn
%O 0,5
%A _Danny Rorabaugh_, Sep 15 2015
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