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 A283101 Numbers of A'Campo forests of degree n>2 and co-dimension 3. 3
 0, 0, 4, 344, 8760, 157504, 2388204, 32737984, 419969088, 5141235840, 60795581132, 700024311536, 7892352548080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS We can prove this using generating functions. REFERENCES P. Flajolet R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009) LINKS N. Combe, V. JugĂ©, 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}'(3,n)x^{3}y^{n} and N_{1}'(3,n) is the number of A'Campo forests with co-dimension 3; N_{3}(x,y)=\sum_{n}N_{3}'(3,n)x^{3}y^{n} where N_{3}'(3,n) is the number of partial configurations. EXAMPLE For n=3, there exist four A'Campo forests of co-dimension 3 and degree 3. For n=2 there do not exist any A'Campo forests of co-dimension 3. CROSSREFS Sequence in context: A317058 A317357 A069884 * A074844 A225207 A052391 Adjacent sequences:  A283098 A283099 A283100 * A283102 A283103 A283104 KEYWORD nonn AUTHOR Noemie Combe, Feb 28 2017 STATUS approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)