A290646 Number of dissections of an n-gon into 3- and 4-gons counted up to rotations and reflections.

1, 2, 2, 7, 14, 53, 171, 691, 2738, 11720, 50486, 224012, 1005468, 4581815, 21093190, 98093226, 459986674, 2173599817, 10340539744, 49496519950, 238240366274, 1152543685463, 5601603835982, 27341242042238, 133977037982121, 658902522544060, 3251446102879398

Offset: 3

Author

Evgeniy Krasko, Sep 03 2017

Keywords

• nonn

Examples

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

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.
• Vladimir Shevelev, On a Luschny question, arXiv:1708.08096 [math.NT], 2017.

Crossrefs

Cf. A001004 (counted distinctly).

Cf. A001002, A290571, A295260, A295419.

Programs

Mathematica

(* See A295419 for DissectionsModDihedral. *)
DissectionsModDihedral[Boole[# == 3 || # == 4]& /@ Range[1, 30]] (* Jean-François Alcover, Sep 25 2019, after Andrew Howroyd *)

PARI

\\ See A295419 for DissectionsModDihedral.
DissectionsModDihedral(apply(v->v==3||v==4, [1..25])) \\ Andrew Howroyd, Nov 22 2017

Extensions

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