OFFSET
1,4
COMMENTS
We can prove this using generating functions.
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}'(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
KEYWORD
nonn,more
AUTHOR
Noemie Combe, Feb 28 2017
STATUS
approved