cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A283102 #16 Mar 02 2017 21:13:21
%S A283102 0,0,0,80,4845,138792,2893338,50507680,787265325,11345154600,
%T A283102 154362306956,2010147294672,25288375607950
%N A283102 Number of A'Campo forests of degree n and co-dimension 4.
%C A283102 We can prove this using generating functions.
%D A283102 P. Flajolet R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009)
%H A283102 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 A283102 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 A283102 For n=1, n=2 and n=3, the number of A'Campo forests of co-dimension 4 is zero.
%e A283102 For n=4 the number of A'Campo forests of co-dimension 4 is 80.
%Y A283102 Cf. A283049, A277877, A283101, A283102, A283103.
%K A283102 nonn,more
%O A283102 1,4
%A A283102 _Noemie Combe_, Feb 28 2017