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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.
1
1, 3264, 168399, 2584576, 21328125, 119952576, 518949739, 1853620224, 5718836601, 15715000000, 39312710151, 90985918464, 197228242549, 404268317376, 789541171875, 1478257278976, 2666742760689, 4654606866624, 7888229913151, 13018560000000
OFFSET
1,2
REFERENCES
W. Fulton, Intersection Theory 2.ed., Springer-Verlag, 1998, page 192.
LINKS
David Eisenbud and Brady Haran, The Journey to 3264, Numberphile video (2023).
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
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 (Steiner's conic problem).
CROSSREFS
Sequence in context: A358870 A337792 A251277 * A286008 A220594 A101706
KEYWORD
nonn,easy
AUTHOR
STATUS
approved