A290722 Number of dissections of a 2n-gon into polygons with even number of sides counted up to rotations and reflections.

1, 2, 4, 13, 48, 238, 1325, 8297, 54519, 373363, 2621872, 18797682, 136969519, 1011903735, 7564219361, 57129086391, 435394899361, 3345082819597, 25885718422329, 201619294539406, 1579629974876090, 12442262963919863, 98483477967355109, 783017782731507416

Offset

2,2

Links

Andrew Howroyd, Table of n, a(n) for n = 2..200

Evgeniy Krasko, Alexander 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(4) = 4 the dissections of an octagon are: two dissections into 3 quadrangles; a dissection into one hexagon and one quadrangle; a dissection into one octagon.

Prog

(PARI) \\ See A295419 for DissectionsModDihedral().
select(v->v>0, DissectionsModDihedral(apply(v->v%2==0, [1..50]))) \\ Andrew Howroyd, Nov 22 2017

Crossrefs

Cf. A003168 (counted distinctly).

Cf. A001004, A290816, A295419.

Sequence in context: A362642 A334444 A268951 * A341378 A058134 A246012

Adjacent sequences: A290719 A290720 A290721 * A290723 A290724 A290725

Keyword

nonn

Author

Evgeniy Krasko, Sep 03 2017

Extensions

Terms a(8) and beyond from Andrew Howroyd, Nov 22 2017

Status

approved