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 A262232 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. 3
 0, 0, 0, 1, 2, 4, 9, 15, 30, 54, 101, 181, 344, 624, 1173, 2183, 4106, 7702, 14591, 27585, 52476, 99868, 190733, 364711, 699238, 1342170, 2581413, 4971053, 9587564, 18512776, 35792551, 69273651, 134219778, 260301158 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS A reflex angle is an angle with measure greater than Pi or 180°. Every polygon has at least three angles with measure less than Pi or 180°. LINKS Danny Rorabaugh, Table of n, a(n) for n = 0..500 Danny Rorabaugh, Polygon demonstration of a(6)=9 FORMULA a(n) = A000031(n) - 2 - floor(n/2), n>0. EXAMPLE Let 1s represent black beads and 0s 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. PROG (Sage) [sum([Necklaces([n-k, k]).cardinality()  for k in range(n-2)]) for n in range(34)] CROSSREFS Cf. A000031, A227910. Sequence in context: A085683 A083270 A000879 * A321410 A218912 A230868 Adjacent sequences:  A262229 A262230 A262231 * A262233 A262234 A262235 KEYWORD nonn AUTHOR Danny Rorabaugh, Sep 15 2015 STATUS approved

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Last modified January 17 16:50 EST 2019. Contains 319235 sequences. (Running on oeis4.)