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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005034 Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals up to rotation.
(Formerly M1768)
7
1, 1, 1, 2, 7, 25, 108, 492, 2431, 12371, 65169, 350792, 1926372, 10744924, 60762760, 347653944, 2009690895, 11723100775, 68937782355, 408323229930, 2434289046255, 14598011263089, 88011196469040, 533216750567280, 3245004785069892, 19829768942544276, 121639211516546668 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also, with a different offset, number of colored quivers in the 2-mutation class of a quiver of Dynkin type A_n. - N. J. A. Sloane, Jan 22 2013

Closed formula is given in my paper linked below. - Nikos Apostolakis, Aug 01 2018

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 290.

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Nikos Apostolakis, Non-crossing trees, quadrangular dissections, ternary trees, and duality preserving bijections, arXiv:1807.11602 [math.CO], July 2018.

F. Harary, E. M. Palmer, R. C. Read, On the cell-growth problem for arbitrary polygons, computer printout, circa 1974

F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Quebec 16 (1992), no 1, 53-80.

P. Leroux and B. Miloudi, Généralisations de la formule d'Otter, Ann. Sci. Math. Québec, Vol. 16, No. 1, pp. 53-80, 1992. (Annotated scanned copy)

Alexander Stoimenow, On the number of chord diagrams, Discr. Math. 218 (2000), 209-233. See p. 232.

Torkildsen, Hermund A., Colored quivers of type A and the cell-growth problem, J. Algebra and Applications, 12 (2013), #1250133.

FORMULA

a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi) * n^(5/2) * 2^(2*n + 3)). - Vaclav Kotesovec, Mar 13 2016

MATHEMATICA

p=4; Table[Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) +If[OddQ[n], 0, Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1}]], {n, 1, 20}] (* Robert A. Russell, Dec 11 2004 *)

CROSSREFS

Column k=4 of A295224.

Sequence in context: A150531 A150532 A074420 * A245157 A150533 A150534

Adjacent sequences:  A005031 A005032 A005033 * A005035 A005036 A005037

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Name clarified by Andrew Howroyd, Nov 20 2017

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 12 16:45 EST 2019. Contains 329058 sequences. (Running on oeis4.)