

A283101


Numbers of A'Campo forests of degree n>2 and codimension 3.


3



0, 0, 4, 344, 8760, 157504, 2388204, 32737984, 419969088, 5141235840, 60795581132, 700024311536, 7892352548080
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OFFSET

1,3


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. JugĂ©, Counting bicolored 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 (1N_{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 codimension 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 codimension 3 and degree 3.
For n=2 there do not exist any A'Campo forests of codimension 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



