

A295622


Number of nonequivalent dissections of an ngon 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
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OFFSET

5,1


LINKS



FORMULA

G.f.: x^5*(3 + 5*x  x^2  x^3) / ((1  x)^4*(1 + x)^2).
a(n) = (n4)*(5 + (1)^n  4*n + 2*n^2) / 8 for n>4.
a(n) = 2*a(n1) + a(n2)  4*a(n3) + a(n4) + 2*a(n5)  a(n6) for n>10.
(End)
a(n) = Sum_{k=0..n5} 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



KEYWORD

nonn


AUTHOR



STATUS

approved



