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A283102 Number of A'Campo forests of degree n and co-dimension 4. 3
0, 0, 0, 80, 4845, 138792, 2893338, 50507680, 787265325, 11345154600, 154362306956, 2010147294672, 25288375607950 (list; graph; refs; listen; history; text; internal format)
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. Jugé, 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}'(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.

EXAMPLE

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

For n=4 the number of A'Campo forests of co-dimension 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

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)