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

3,2

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.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001004 (counted distinctly).

Cf. A001002, A290571, A295260, A295419.

Sequence in context: A379566 A061575 A306009 * A133602 A137249 A216461

Adjacent sequences: A290643 A290644 A290645 * A290647 A290648 A290649

Keyword

nonn

Author

Evgeniy Krasko, Sep 03 2017

Extensions

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

Status

approved