A277877 Number of A'Campo forests of degree n>1 and co-dimension 2.

0, 30, 608, 8740, 109296, 1269450, 14096320, 151927776, 1603346160, 16659866938, 171064877280

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. Jugé, Counting bi-colored 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 (1-N_{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 co-dimension 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 co-dimension 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