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A005038 Number of ways of dissecting a polygon into n hexagons.
(Formerly M2026)
5
1, 1, 2, 12, 57, 366, 2340, 16252, 115940, 854981, 6444826, 49554420, 387203390, 3068067060, 24604111560, 199398960212, 1631041938108, 13451978877748, 111765327780200, 934774244822704, 7865200653146905 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Also, with a different offset, number of colored quivers in the 3-mutation class of a quiver of Dynkin type A_n. - N. J. A. Sloane, Jan 22 2013

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

Hermund A. Torkildsen, Colored quivers of type A and the cell-growth problem, J. Algebra and Applications, 12 (2013), #1250133. - From N. J. A. Sloane, Jan 22 2013

FORMULA

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], 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

Cf. A001683, A005034.

Sequence in context: A180073 A067125 A177782 * A094780 A268594 A100103

Adjacent sequences:  A005035 A005036 A005037 * A005039 A005040 A005041

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(21) corrected by Sean A. Irvine, Mar 11 2016

STATUS

approved

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Last modified June 28 20:39 EDT 2017. Contains 288840 sequences.