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 A290646 Number of dissections of an n-gon into 3- and 4-gons counted up to rotations and reflections. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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: A061274 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

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Last modified April 17 08:00 EDT 2024. Contains 371756 sequences. (Running on oeis4.)