

A262232


Number of black and white nbead necklaces with at least 3 white beads (turning over is not allowed); also number of clockwise arrangements of reflex and nonreflex angles that can form an ngon.


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
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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([nk, k]).cardinality() for k in range(n2)]) 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



