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A005040 Number of nonequivalent dissections of a polygon into n pentagons by nonintersecting diagonals up to rotation and reflection.
(Formerly M1851)
6
1, 1, 2, 8, 33, 194, 1196, 8196, 58140, 427975, 3223610, 24780752, 193610550, 1534060440, 12302123640, 99699690472, 815521503060, 6725991120004, 55882668179880, 467387136083296, 3932600361607809, 33269692212847056, 282863689410850236, 2415930985594609548 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

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 = 1..1000

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.

E. V. Konstantinova, A survey of the cell-growth problem and some its variations, preprint, 2001.

E. V. Konstantinova, Com2Mac - Preprints [Dead link?]

FORMULA

See Mathematica code.

a(n) ~ 2^(8*n - 1/2) / (sqrt(Pi) * n^(5/2) * 3^(3*n + 5/2)). - Vaclav Kotesovec, Mar 13 2016

MATHEMATICA

p=5; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) + If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)], 3Binomial[(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, 2}]])/2, {n, 1, 20}] (* Robert A. Russell, Dec 11 2004 *)

CROSSREFS

Column k=5 of A295260.

Cf. A005419, A004127, A005036, A000207.

Sequence in context: A030821 A236382 A269890 * A191551 A263627 A172448

Adjacent sequences:  A005037 A005038 A005039 * A005041 A005042 A005043

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sascha Kurz, Oct 13 2001

Name edited by Andrew Howroyd, Nov 20 2017

STATUS

approved

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Last modified September 20 22:20 EDT 2018. Contains 315247 sequences. (Running on oeis4.)