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%I #29 Sep 25 2019 05:56:50
%S 1,1,2,4,8,23,65,223,757,2824,10559,40994,160734,641420,2584587,
%T 10528305,43237978,178974779,745814185,3127246179,13185588894,
%U 55878618492,237905685582,1017225981255,4366536472758,18812074137141,81320795918871,352638701880227
%N Number of dissections of an n-gon into polygons with odd number of sides counted up to rotations and reflections.
%H Andrew Howroyd, <a href="/A290816/b290816.txt">Table of n, a(n) for n = 3..200</a>
%H E. Krasko, A. Omelchenko, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i1p17">Brown's Theorem and its Application for Enumeration of Dissections and Planar Trees</a>, The Electronic Journal of Combinatorics, 22 (2015), #P1.17.
%e For a(5) = 2 the dissections of a pentagon are: a dissection into 3 triangles; a dissection into one pentagon.
%t (* See A295419 for DissectionsModDihedral *)
%t DissectionsModDihedral[Mod[#, 2]& /@ Range[1, 31]] (* _Jean-François Alcover_, Sep 25 2019, after _Andrew Howroyd_ *)
%o (PARI) \\ See A295419 for DissectionsModDihedral().
%o DissectionsModDihedral(apply(v->v%2, [1..25])) \\ _Andrew Howroyd_, Nov 22 2017
%Y Cf. A049124 (counted distinctly).
%Y Cf. A001004, A290722, A295419.
%K nonn
%O 3,3
%A _Evgeniy Krasko_, Sep 03 2017
%E Terms a(16) and beyond from _Andrew Howroyd_, Nov 22 2017