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A003456 Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation and reflection.
(Formerly M1509)
5

%I M1509

%S 1,2,5,17,62,275,1272,6225,31075,158376,816229,4251412,22319056,

%T 117998524,627573216,3355499036,18025442261,97239773408,526560862829,

%U 2861189112867,15595669996482,85252072993968,467247847612316,2567091151780343

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

%C Total number of dissections of a n-gon into 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="/A003456/b003456.txt">Table of n, a(n) for n = 3..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 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 DissectionsModDihedralRooted(apply(i->1, [1..30]))

%Y Cf. A001004, A003454, A003455, A005035, A295259.

%K nonn

%O 3,2

%A _N. J. A. Sloane_

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

%E Name clarified by _Andrew Howroyd_, Nov 24 2017

%E a(15) corrected by _Andrew Howroyd_, Nov 24 2017

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)