

A003443


Number of nonequivalent dissections of an ngon into n4 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 ngon into n4 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 n5 triangles or 2 quadrilaterals and n6 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

Andrew Howroyd, Table of n, a(n) for n = 5..200
P. Lisonek, Closed forms for the number of polygon dissections, Journal of Symbolic Computation 20 (1995), 595601.
C. R. Read, On general dissections of a polygon, Aequat. math. 18 (1978) 370388.


PROG

(PARI) \\ See A003442 for DissectionsModCyclicRooted()
{ my(v=DissectionsModCyclicRooted(apply(i>if(i>=3&&i<=5, y^(i3) + O(y^3)), [1..30]))); apply(p>polcoeff(p, 2), v[5..#v]) } \\ Andrew Howroyd, Nov 22 2017


CROSSREFS

Cf. A003442, A003454.
Sequence in context: A226511 A125651 A043017 * A119581 A240916 A006292
Adjacent sequences: A003440 A003441 A003442 * A003444 A003445 A003446


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Sean A. Irvine, May 05 2015
Name clarified and offset changed by Andrew Howroyd, Nov 22 2017


STATUS

approved



