|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
REFERENCES
|
W. Fulton, Intersection Theory 2.ed., Springer-Verlag, 1998, page 192.
|
|
LINKS
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|