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A003448 Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.
(Formerly M2993)
3
1, 3, 15, 81, 422, 2124, 10223, 47813, 218130, 977354, 4315130, 18833538, 81424236, 349303352, 1488748719, 6310303727, 26621551418, 111854042306, 468309841090, 1954642186302, 8136002036672, 33782928166668, 139971138117190, 578803145957026 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

Number of dissections of regular n-gon into n-4 polygons with reflection and rooted at a cell.- Sean A. Irvine, May 13 2015

The dissection will always be composed of either 1 pentagon and n-5 triangles or 2 quadrilaterals and n-6 triangles. - Andrew Howroyd, Nov 24 2017

REFERENCES

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 5..200

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

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

PROG

(PARI) \\ See A003447 for DissectionsModDihedralRooted()

my(v=DissectionsModDihedralRooted(apply(i->if(i>=3&&i<=5, y^(i-3)+O(y^3)), [1..30]))); apply(p->polcoeff(p, 2), v[5..#v]) \\ Andrew Howroyd, Nov 24 2017

CROSSREFS

Cf. A003447.

Sequence in context: A020044 A024338 A253774 * A229841 A198628 A233020

Adjacent sequences:  A003445 A003446 A003447 * A003449 A003450 A003451

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, May 13 2015

Name clarified by Andrew Howroyd, Nov 24 2017

STATUS

approved

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Last modified March 19 11:10 EDT 2019. Contains 321329 sequences. (Running on oeis4.)