A003443 Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation. (Formerly M3104)

1, 3, 24, 150, 825, 4205, 20384, 95472, 436050, 1954150, 8629528, 37665030, 162845865, 698599125, 2977488000, 12620579140, 53243068230, 223707978090, 936619554000, 3909283969500, 16272003594658, 67565854800378, 279942274434624

Offset

5,2

Comments

Number of dissections of regular n-gon into n-4 polygons without reflection and rooted at a cell. - Sean A. Irvine, May 05 2015

The conditions imposed mean that the dissection will always be composed of either 1 pentagon and n-5 triangles or 2 quadrilaterals and n-6 triangles. - Andrew Howroyd, Nov 23 2017

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Andrew Howroyd, Table of n, a(n) for n = 5..200

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.

Prog

(PARI) \\ See A003442 for DissectionsModCyclicRooted()
{ my(v=DissectionsModCyclicRooted(apply(i->if(i>=3&&i<=5, y^(i-3) + O(y^3)), [1..30]))); apply(p->polcoeff(p, 2), v[5..#v]) } \\ Andrew Howroyd, Nov 22 2017

Crossrefs

Cf. A003442, A003454.

Sequence in context: A226511 A125651 A043017 * A119581 A367119 A240916

Adjacent sequences: A003440 A003441 A003442 * A003444 A003445 A003446

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, May 05 2015

Name clarified and offset changed by Andrew Howroyd, Nov 22 2017

Status

approved