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A295622 Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation. 2
3, 11, 24, 46, 75, 117, 168, 236, 315, 415, 528, 666, 819, 1001, 1200, 1432, 1683, 1971, 2280, 2630, 3003, 3421, 3864, 4356, 4875, 5447, 6048, 6706, 7395, 8145, 8928, 9776, 10659, 11611, 12600, 13662, 14763, 15941, 17160, 18460, 19803, 21231, 22704, 24266 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,1
LINKS
P. Lisonek, Closed forms for the number of polygon dissections, Journal of Symbolic Computation 20 (1995), 595-601.
Ronald C. Read, On general dissections of a polygon, Aequat. math. 18 (1978) 370-388.
FORMULA
Conjectures from Colin Barker, Nov 25 2017: (Start)
G.f.: x^5*(3 + 5*x - x^2 - x^3) / ((1 - x)^4*(1 + x)^2).
a(n) = (n-4)*(-5 + (-1)^n - 4*n + 2*n^2) / 8 for n>4.
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.
(End)
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
PROG
(PARI) \\ See A003442 for DissectionsModCyclicRooted()
{ my(v=DissectionsModCyclicRooted(apply(i->y + O(y^4), [1..40]))); apply(p->polcoeff(p, 3), v[5..#v]) }
CROSSREFS
Sequence in context: A293404 A293414 A212252 * A294415 A141595 A112051
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Nov 24 2017
STATUS
approved

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Last modified June 12 13:39 EDT 2024. Contains 373331 sequences. (Running on oeis4.)