

A283102


Number of A'Campo forests of degree n and codimension 4.


3



0, 0, 0, 80, 4845, 138792, 2893338, 50507680, 787265325, 11345154600, 154362306956, 2010147294672, 25288375607950
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OFFSET

1,4


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}'(4,n)x^{4}y^{n} and N_{1}'(4,n) is the number of A'Campo forests with codimension 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 codimension 4 is zero.
For n=4 the number of A'Campo forests of codimension 4 is 80.


CROSSREFS

Cf. A283049, A277877, A283101, A283102, A283103.
Sequence in context: A203171 A076004 A216987 * A259076 A190931 A006202
Adjacent sequences: A283099 A283100 A283101 * A283103 A283104 A283105


KEYWORD

nonn,more


AUTHOR

Noemie Combe, Feb 28 2017


STATUS

approved



