A283103 Number of A'Campo forests of degree n and co-dimension 5.

0, 0, 0, 4, 1380, 75600, 2340744, 54275296, 1055436228, 18230184752, 289150871152, 4300858168200, 60843411796440

Offset

1,4

Comments

a(n) is the number of A'Campo forests of degree n and of co-dimension 5.

References

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

Links

Table of n, a(n) for n=1..13.

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}'(5,n)x^{5}y^{n} and N_{1}'(5,n) is the number of A'Campo forests with co-dimension 5; N_{2}(x,y)=\sum_{n}N_{2}'(5,n)x^{5}y^{n} where N_{2}'(5,n) is the number of partial configurations.

Example

For n<4, the number of A'Campo forests of degree n  and co-dimension 5 is zero.
For n = 4 the number of A'Campo forests of co-dimension 5 is 4.

Crossrefs

Cf. A283101, A283102, A283049, A277877.

Sequence in context: A172925 A167071 A274296 * A278844 A036107 A201390

Adjacent sequences: A283100 A283101 A283102 * A283104 A283105 A283106

Keyword

nonn

Author

Noemie Combe, Feb 28 2017

Extensions

Added crossrefs

Status

approved