A003456 Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation and reflection.

1, 2, 5, 17, 62, 275, 1272, 6225, 31075, 158376, 816229, 4251412, 22319056, 117998524, 627573216, 3355499036, 18025442261, 97239773408, 526560862829, 2861189112867, 15595669996482, 85252072993968, 467247847612316, 2567091151780343

Offset: 3

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Total number of dissections of an n-gon into polygons with reflection and rooted at a cell. - Sean A. Irvine, May 14 2015

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 = 3..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. A001004, A003454, A003455, A005035, A295259.

Programs

PARI

\\ See A003447 for DissectionsModDihedralRooted()
DissectionsModDihedralRooted(apply(i->1, [1..30]))

Extensions

More terms from Sean A. Irvine, May 14 2015

Name clarified by Andrew Howroyd, Nov 24 2017

a(15) corrected by Andrew Howroyd, Nov 24 2017