OFFSET
4,2
COMMENTS
Number of dissections of regular n-gon into n-3 polygons with reflection and rooted at a cell. - Sean A. Irvine, May 13 2015
The dissection will always be composed of one quadrilateral and n-4 triangles. - Andrew Howroyd, Nov 24 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 = 4..200
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)
DissectionsModDihedralRooted(v)={my(n=#v);
my(q=vector(n)); q[1]=serreverse(x-sum(i=3, #v, x^i*v[i])/x + O(x*x^n));
for(i=2, n, q[i]=q[i-1]*q[1]);
my(vars=variables(q[1]));
my(u(m, r)=substvec(q[r]+O(x^(n\m+1)), vars, apply(t->t^m, vars)));
my(R=sum(i=1, (#v-1)\2, v[2*i+1]*u(2, i)), Q=sum(i=2, #v\2, v[2*i]*u(2, i-1)), T=sum(i=3, #v, my(c=v[i]); if(c, c*sumdiv(i, d, eulerphi(d)*u(d, i/d))/i)));
my(p=O(x*x^n) + (R*(x+R)/(1-Q) + Q*(u(2, 1)+(x+R)^2/(1-Q)^2)/2 + T)/2);
vector(n, i, polcoeff(p, i))}
my(v=DissectionsModDihedralRooted(apply(i->if(i>=3&&i<=4, y^(i-3)+O(y^2)), [1..25]))); apply(p->polcoeff(p, 1), v[4..#v])
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, May 13 2015
Name clarified by Andrew Howroyd, Nov 24 2017
STATUS
approved