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

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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Cf. A003442, A003454.

Programs

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

Extensions

More terms from Sean A. Irvine, May 05 2015

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