login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

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}'(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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 16 13:24 EST 2018. Contains 318167 sequences. (Running on oeis4.)