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A003443 Number of nonequivalent dissections of an n-gon into n-4 polygons by nonintersecting diagonals rooted at a cell up to rotation.
(Formerly M3104)
3
1, 3, 24, 150, 825, 4205, 20384, 95472, 436050, 1954150, 8629528, 37665030, 162845865, 698599125, 2977488000, 12620579140, 53243068230, 223707978090, 936619554000, 3909283969500, 16272003594658, 67565854800378, 279942274434624 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,2
COMMENTS
Number of dissections of regular n-gon into n-4 polygons without reflection and rooted at a cell. - Sean A. Irvine, May 05 2015
The conditions imposed mean that the dissection will always be composed of either 1 pentagon and n-5 triangles or 2 quadrilaterals and n-6 triangles. - Andrew Howroyd, Nov 23 2017
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
P. Lisonek, Closed forms for the number of polygon dissections, Journal of Symbolic Computation 20 (1995), 595-601.
Ronald C. Read, On general dissections of a polygon, Aequat. math. 18 (1978) 370-388.
PROG
(PARI) \\ See A003442 for DissectionsModCyclicRooted()
{ my(v=DissectionsModCyclicRooted(apply(i->if(i>=3&&i<=5, y^(i-3) + O(y^3)), [1..30]))); apply(p->polcoeff(p, 2), v[5..#v]) } \\ Andrew Howroyd, Nov 22 2017
CROSSREFS
Sequence in context: A226511 A125651 A043017 * A119581 A367119 A240916
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, May 05 2015
Name clarified and offset changed by Andrew Howroyd, Nov 22 2017
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)