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A277877 Number of A'Campo forests of degree n>1 and co-dimension 2. 3
0, 30, 608, 8740, 109296, 1269450, 14096320, 151927776, 1603346160, 16659866938, 171064877280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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..11.

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}'(2,n)x^{2}y^{n} and N_{1}'(2,n) is the number of A'Campo forests with co-dimension 2; N_{2}(x,y)=\sum_{n}N_{2}'(2,n)x^{2}y^{n} where N_{2}'(2,n) is the number of partial configurations.

EXAMPLE

For n=3 we have a(3)=30 A'Campo forests of co-dimension 2.

CROSSREFS

Sequence in context: A020980 A051303 A020975 * A279870 A124099 A028258

Adjacent sequences:  A277874 A277875 A277876 * A277878 A277879 A277880

KEYWORD

nonn,more

AUTHOR

Noemie Combe, Feb 27 2017

STATUS

approved

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Last modified January 21 02:59 EST 2019. Contains 319344 sequences. (Running on oeis4.)