login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
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 * A218912 A230868 A014290

Adjacent sequences:  A262229 A262230 A262231 * A262233 A262234 A262235

KEYWORD

nonn

AUTHOR

Danny Rorabaugh, Sep 15 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 18 20:32 EST 2018. Contains 299330 sequences. (Running on oeis4.)