Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A003444
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A003444 Number of dissections of a polygon.
(Formerly M3455)
+0
6
1, 4, 12, 43, 143, 504, 1768, 6310, 22610, 81752, 297160, 1086601, 3991995, 14732720, 54587280, 202997670, 757398510, 2834510744, 10637507400, 40023636310, 150946230006, 570534578704, 2160865067312, 8199711378716 (list; graph; listen)
OFFSET

4,2

COMMENT

Also number of necklaces of 2 colors with 2n beads and n-2 black ones. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2002

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

P. Lisonek, Closed forms for the number of polygon dissections. Journal of Symbolic Computation 20 (1995), 595-601.

R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.

FORMULA

(1/(2n)) Sum_{d |(2n, k)} phi(d)*binomial(2n/d, k/d) with k=n-2 - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2002

MATHEMATICA

Table[(Plus@@(EulerPhi[ # ]Binomial[2n/#, (n-2)/# ] &)/@Intersection[Divisors[2n], Divisors[n-2]])/(2n), {n, 3, 32}]

CROSSREFS

Cf. A047996, A073020.

Sequence in context: A149352 A149353 A149354 this_sequence A149355 A149356 A149357

Adjacent sequences: A003441 A003442 A003443 this_sequence A003445 A003446 A003447

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2002

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


AT&T Labs Research