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A003452 Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.
(Formerly M1742)
3

%I M1742

%S 2,7,15,28,45,69,98,136,180,235,297,372,455,553,660,784,918,1071,1235,

%T 1420,1617,1837,2070,2328,2600,2899,3213,3556,3915,4305,4712,5152,

%U 5610,6103,6615,7164,7733,8341,8970,9640,10332,11067,11825,12628

%N Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation and reflection.

%C Number of dissections of regular n-gon into 3 polygons with reflection and rooted at a cell. - _Sean A. Irvine_, May 14 2015

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

%H Andrew Howroyd, <a href="/A003452/b003452.txt">Table of n, a(n) for n = 5..500</a>

%H P. Lisonek, <a href="http://dx.doi.org/10.1006/jsco.1995.1066">Closed forms for the number of polygon dissections</a>, Journal of Symbolic Computation 20 (1995), 595-601.

%H C. R. Read, <a href="http://dx.doi.org/10.1007/BF03031688">On general dissections of a polygon</a>, Aequat. math. 18 (1978) 370-388.

%o (PARI) \\ See A003447 for DissectionsModDihedralRooted()

%o { my(v=DissectionsModDihedralRooted(apply(i->y+O(y^4), [1..40]))); apply(p->polcoeff(p, 3), v[5..#v]) } \\ _Andrew Howroyd_, Nov 24 2017

%Y Cf. A003447.

%K nonn

%O 5,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, May 14 2015

%E Name clarified by _Andrew Howroyd_, Nov 24 2017

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Last modified April 20 16:17 EDT 2019. Contains 322310 sequences. (Running on oeis4.)