A003456 Number of nonequivalent dissections of an n-gon by nonintersecting diagonals rooted at a cell up to rotation and reflection. (Formerly M1509)

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

3,2

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.

Prog

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

Crossrefs

Cf. A001004, A003454, A003455, A005035, A295259.

Sequence in context: A148415 A148416 A259792 * A109084 A217596 A090902

Adjacent sequences: A003453 A003454 A003455 * A003457 A003458 A003459

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved