A283101 Numbers of A'Campo forests of degree n>2 and co-dimension 3.

0, 0, 4, 344, 8760, 157504, 2388204, 32737984, 419969088, 5141235840, 60795581132, 700024311536, 7892352548080

Offset: 1

Author

Noemie Combe, Feb 28 2017

Keywords

• nonn

Comments

We can prove this using generating functions.

Examples

			For n=3, there exist four A'Campo forests of co-dimension 3 and degree 3.
For n=2 there do not exist any A'Campo forests of co-dimension 3.
		

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}'(3,n)x^{3}y^{n} and N_{1}'(3,n) is the number of A'Campo forests with co-dimension 3; N_{3}(x,y)=\sum_{n}N_{3}'(3,n)x^{3}y^{n} where N_{3}'(3,n) is the number of partial configurations.