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Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation.
(Formerly M3104)
3

%I M3104 #34 Jan 19 2021 11:48:00

%S 1,3,24,150,825,4205,20384,95472,436050,1954150,8629528,37665030,

%T 162845865,698599125,2977488000,12620579140,53243068230,223707978090,

%U 936619554000,3909283969500,16272003594658,67565854800378,279942274434624

%N Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation.

%C Number of dissections of regular n-gon into n-4 polygons without reflection and rooted at a cell. - _Sean A. Irvine_, May 05 2015

%C The conditions imposed mean that the dissection will always be composed of either 1 pentagon and n-5 triangles or 2 quadrilaterals and n-6 triangles. - _Andrew Howroyd_, Nov 23 2017

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

%H Andrew Howroyd, <a href="/A003443/b003443.txt">Table of n, a(n) for n = 5..200</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 Ronald C. 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 A003442 for DissectionsModCyclicRooted()

%o { my(v=DissectionsModCyclicRooted(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 22 2017

%Y Cf. A003442, A003454.

%K nonn

%O 5,2

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, May 05 2015

%E Name clarified and offset changed by _Andrew Howroyd_, Nov 22 2017