A283102 Number of A'Campo forests of degree n and co-dimension 4.

0, 0, 0, 80, 4845, 138792, 2893338, 50507680, 787265325, 11345154600, 154362306956, 2010147294672, 25288375607950

Offset

1,4

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..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}'(4,n)x^{4}y^{n} and N_{1}'(4,n) is the number of A'Campo forests with co-dimension 4; N_{2}(x,y)=\sum_{n}N_{2}'(4,n)x^{4}y^{n} where N_{2}'(4,n) is the number of partial configurations.

Example

For n=1, n=2 and n=3, the number of A'Campo forests of co-dimension 4 is zero.
For n=4 the number of A'Campo forests of co-dimension 4 is 80.

Crossrefs

Cf. A283049, A277877, A283101, A283102, A283103.

Sequence in context: A203171 A076004 A216987 * A259076 A335610 A190931

Adjacent sequences: A283099 A283100 A283101 * A283103 A283104 A283105

Keyword

nonn,more

Author

Noemie Combe, Feb 28 2017

Status

approved