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A283102 Number of A'Campo forests of degree n and co-dimension 4. 3

%I

%S 0,0,0,80,4845,138792,2893338,50507680,787265325,11345154600,

%T 154362306956,2010147294672,25288375607950

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

%C We can prove this using generating functions.

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

%H N. Combe, V. Jugé, <a href="https://arxiv.org/abs/1702.07672">Counting bi-colored A'Campo forests</a> arXiv:1702.07672 [Math.AG], 2017.

%F 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.

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

%e For n=4 the number of A'Campo forests of co-dimension 4 is 80.

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

%K nonn,more

%O 1,4

%A _Noemie Combe_, Feb 28 2017

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Last modified January 27 08:31 EST 2020. Contains 331293 sequences. (Running on oeis4.)