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

Author

Noemie Combe, Feb 27 2017

Keywords

• nonn
• more

Comments

We can prove this using generating functions.

Examples

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

References

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

Links

• 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.