

A005036


Number of nonequivalent dissections of a polygon into n quadrilaterals by nonintersecting diagonals up to rotation and reflection.
(Formerly M1491)


5



1, 1, 2, 5, 16, 60, 261, 1243, 6257, 32721, 175760, 963900, 5374400, 30385256, 173837631, 1004867079, 5861610475, 34469014515, 204161960310, 1217145238485, 7299007647552, 44005602441840
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OFFSET

1,3


COMMENTS

The subsequence of primes begins: 2, 5, 6257, no more through a(100).  Jonathan Vos Post, Apr 08 2011
Closed formula is given in my paper linked below.  Nikos Apostolakis, Aug 01 2018


REFERENCES

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


LINKS

T. D. Noe, Table of n, a(n) for n = 1..100
Nikos Apostolakis, Noncrossing 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 cellgrowth problem for arbitrary polygons, computer printout, circa 1974
F. Harary, E. M. Palmer and R. C. Read, On the cellgrowth problem for arbitrary polygons, Discr. Math. 11 (1975), 371389.
E. V. Konstantinova, A survey of the cellgrowth problem and some its variations, Com 2 MaCKOSEF, 2001.
Index entries for "core" sequences


FORMULA

a(n) ~ 3^(3*n + 1/2) / (sqrt(Pi) * n^(5/2) * 2^(2*n + 4)).  Vaclav Kotesovec, Mar 13 2016


MATHEMATICA

p=4; Table[(Binomial[(p1)n, n]/(((p2)n+1)((p2)n+2)) + If[OddQ[n], If[OddQ[p], Binomial[(p1)n/2, (n1)/2]/n, (p+1)Binomial[((p1)n1)/2, (n1)/2]/((p2)n+2)], 3Binomial[(p1)n/2, n/2]/((p2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p1)n+1)/#, (n1)/# ]/((p1)n+1)&, Complement[Divisors[GCD[p, n1]], {1, 2}]])/2, {n, 1, 20}] (* Robert A. Russell, Dec 11 2004 *)


CROSSREFS

Column k=4 of A295260.
Cf. A005419, A004127, A005038, A005040, A000207.
Sequence in context: A205486 A210668 A279564 * A012051 A012159 A009736
Adjacent sequences: A005033 A005034 A005035 * A005037 A005038 A005039


KEYWORD

core,nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Sascha Kurz, Oct 13 2001
Name edited by Andrew Howroyd, Nov 20 2017


STATUS

approved



