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A283101
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Numbers of A'Campo forests of degree n>2 and co-dimension 3.
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3
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0, 0, 4, 344, 8760, 157504, 2388204, 32737984, 419969088, 5141235840, 60795581132, 700024311536, 7892352548080
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OFFSET
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1,3
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COMMENTS
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We can prove this using generating functions.
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REFERENCES
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P. Flajolet R. Sedgewick, Analytic Combinatorics, Cambridge University Press (2009)
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LINKS
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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