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A290646 Number of dissections of an n-gon into 3- and 4-gons counted up to rotations and reflections.

%I A290646 #82 Sep 25 2019 05:57:27
%S A290646 1,2,2,7,14,53,171,691,2738,11720,50486,224012,1005468,4581815,
%T A290646 21093190,98093226,459986674,2173599817,10340539744,49496519950,
%U A290646 238240366274,1152543685463,5601603835982,27341242042238,133977037982121,658902522544060,3251446102879398
%N A290646 Number of dissections of an n-gon into 3- and 4-gons counted up to rotations and reflections.
%H A290646 Andrew Howroyd, <a href="/A290646/b290646.txt">Table of n, a(n) for n = 3..200</a>
%H A290646 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.
%H A290646 Vladimir Shevelev, <a href="https://arxiv.org/abs/1708.08096">On a Luschny question</a>, arXiv:1708.08096 [math.NT], 2017.
%e A290646 For a(5) = 2 the dissections of a pentagon are: a dissection into 3 triangles; a dissection into one triangle and one quadrangle.
%t A290646 (* See A295419 for DissectionsModDihedral. *)
%t A290646 DissectionsModDihedral[Boole[# == 3 || # == 4]& /@ Range[1, 30]] (* _Jean-François Alcover_, Sep 25 2019, after _Andrew Howroyd_ *)
%o A290646 (PARI) \\ See A295419 for DissectionsModDihedral.
%o A290646 DissectionsModDihedral(apply(v->v==3||v==4, [1..25])) \\ _Andrew Howroyd_, Nov 22 2017
%Y A290646 Cf. A001004 (counted distinctly).
%Y A290646 Cf. A001002, A290571, A295260, A295419.
%K A290646 nonn
%O A290646 3,2
%A A290646 _Evgeniy Krasko_, Sep 03 2017
%E A290646 Terms a(16) and beyond from _Andrew Howroyd_, Nov 22 2017