

A277877


Number of A'Campo forests of degree n>1 and codimension 2.


3



0, 30, 608, 8740, 109296, 1269450, 14096320, 151927776, 1603346160, 16659866938, 171064877280
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

We can prove this using generating functions.


REFERENCES

P. Flajolet R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009)


LINKS

Table of n, a(n) for n=1..11.
N. Combe, V. JugĂ©, Counting bicolored A'Campo forests, arXiv:1702.07672 [math.AG], 2017.


FORMULA

a(n) is obtained by using the generating function N_{1} =1+yN_{2}^4 and (1N_{2} +2yN_{2}^4 yN_{2}^{5} +xyN_{2}^{6} +y^{2}N_{2}^{8})(1+yN_{2}^{4}xyN_{2}^{5})+x^3y^{2}N_{2}^{9} =0, where N_{1}(x,y)=\sum_{n}N_{1}'(2,n)x^{2}y^{n} and N_{1}'(2,n) is the number of A'Campo forests with codimension 2; N_{2}(x,y)=\sum_{n}N_{2}'(2,n)x^{2}y^{n} where N_{2}'(2,n) is the number of partial configurations.


EXAMPLE

For n=3 we have a(3)=30 A'Campo forests of codimension 2.


CROSSREFS

Sequence in context: A020980 A051303 A020975 * A279870 A124099 A028258
Adjacent sequences: A277874 A277875 A277876 * A277878 A277879 A277880


KEYWORD

nonn,more


AUTHOR

Noemie Combe, Feb 27 2017


STATUS

approved



