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

Author

Evgeniy Krasko, Sep 03 2017

Keywords

• nonn

Examples

			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.
		

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.

Crossrefs

Cf. A003168 (counted distinctly).

Cf. A001004, A290816, A295419.

Programs

PARI

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

Extensions

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