A290816 Number of dissections of an n-gon into polygons with odd number of sides counted up to rotations and reflections.

1, 1, 2, 4, 8, 23, 65, 223, 757, 2824, 10559, 40994, 160734, 641420, 2584587, 10528305, 43237978, 178974779, 745814185, 3127246179, 13185588894, 55878618492, 237905685582, 1017225981255, 4366536472758, 18812074137141, 81320795918871, 352638701880227

Offset

3,3

Links

Andrew Howroyd, Table of n, a(n) for n = 3..200

E. Krasko, A. Omelchenko, Brown's Theorem and its Application for Enumeration of Dissections and Planar Trees, The Electronic Journal of Combinatorics, 22 (2015), #P1.17.

Example

For a(5) = 2 the dissections of a pentagon are: a dissection into 3 triangles; a dissection into one pentagon.

Mathematica

(* See A295419 for DissectionsModDihedral *)
DissectionsModDihedral[Mod[#, 2]& /@ Range[1, 31]] (* Jean-François Alcover, Sep 25 2019, after Andrew Howroyd *)

Prog

(PARI) \\ See A295419 for DissectionsModDihedral().
DissectionsModDihedral(apply(v->v%2, [1..25])) \\ Andrew Howroyd, Nov 22 2017

Crossrefs

Cf. A049124 (counted distinctly).

Cf. A001004, A290722, A295419.

Sequence in context: A018323 A151380 A295419 * A181070 A226659 A009327

Adjacent sequences: A290813 A290814 A290815 * A290817 A290818 A290819

Keyword

nonn

Author

Evgeniy Krasko, Sep 03 2017

Extensions

Terms a(16) and beyond from Andrew Howroyd, Nov 22 2017

Status

approved