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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
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
P. Lisonek, Closed forms for the number of polygon dissections, Journal of Symbolic Computation 20 (1995), 595-601.
Ronald C. 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
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, May 13 2015
Name clarified by Andrew Howroyd, Nov 24 2017
STATUS
approved