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A328148 The number of conics tangent to five non-singular curves of degree n in general position, in a projective plane defined over an algebraically closed field of characteristic zero. 0
1, 3264, 168399, 2584576, 21328125, 119952576, 518949739, 1853620224, 5718836601, 15715000000, 39312710151, 90985918464, 197228242549, 404268317376, 789541171875, 1478257278976, 2666742760689, 4654606866624, 7888229913151, 13018560000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

W. Fulton, Intersection Theory 2.ed., Springer-Verlag, 1998, page 192.

LINKS

Table of n, a(n) for n=1..20.

Wikipedia, Steiner's conic problem

Wikipedia, Enumerative Geometry

FORMULA

a(n) = n^5 * ((n-1)^5 + 10*(n-1)^4 + 40*(n-1)^3 + 40*(n-1)^2 + 10*(n-1) + 1).

EXAMPLE

a(2)=3264 because there are 3264 conics tangent to five conics in general position (the Steiner's conic problem).

CROSSREFS

Sequence in context: A253857 A337792 A251277 * A286008 A220594 A101706

Adjacent sequences:  A328145 A328146 A328147 * A328149 A328150 A328151

KEYWORD

nonn

AUTHOR

Niccolò Castronuovo, Jun 07 2020

STATUS

approved

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Last modified October 28 04:43 EDT 2021. Contains 348313 sequences. (Running on oeis4.)