%I #25 Mar 19 2021 09:58:02
%S 3,11,24,46,75,117,168,236,315,415,528,666,819,1001,1200,1432,1683,
%T 1971,2280,2630,3003,3421,3864,4356,4875,5447,6048,6706,7395,8145,
%U 8928,9776,10659,11611,12600,13662,14763,15941,17160,18460,19803,21231,22704,24266
%N Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation.
%H Andrew Howroyd, <a href="/A295622/b295622.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 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.
%F Conjectures from _Colin Barker_, Nov 25 2017: (Start)
%F G.f.: x^5*(3 + 5*x - x^2 - x^3) / ((1 - x)^4*(1 + x)^2).
%F a(n) = (n-4)*(-5 + (-1)^n - 4*n + 2*n^2) / 8 for n>4.
%F a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6) for n>10.
%F (End)
%F a(n) = Sum_{k=0..n-5} f(k), where f(n) = Sum_{k=0..n} 3 + lcm(k, 2)) (conjecture). - _Jon Maiga_, Nov 28 2018
%o (PARI) \\ See A003442 for DissectionsModCyclicRooted()
%o { my(v=DissectionsModCyclicRooted(apply(i->y + O(y^4), [1..40]))); apply(p->polcoeff(p, 3), v[5..#v]) }
%Y Cf. A003442, A003451, A003452, A003453.
%K nonn
%O 5,1
%A _Andrew Howroyd_, Nov 24 2017