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A033541
Number of irreducible exceptional curves of first kind on del Pezzo surface of degree 9-n.
0
0, 1, 3, 6, 10, 16, 27, 56, 240
OFFSET
0,3
COMMENTS
The case n=1 is exceptional and a(1) could be 0 or 1.
a(n) is the number of vertices of the uniform (n-4)_21 polytope. - Andrey Zabolotskiy, Oct 29 2018
REFERENCES
Yu. I. Manin, Rational surfaces and Galois cohomology, pp. 495-509 of Proc. International Congress Mathematicians, Moscow 1966.
Yu. I. Manin, Cubic Forms, Second edition, North-Holland Publishing Co., Amsterdam, 1986, page 136, Theorem 26.2(iii), Table (IV.9).
LINKS
M. Nagata, On rational surfaces, I, Mem. Coll. Sci. Univ. Kyoto, Ser. A., XXXII (No. 3, 1960).
M. Nagata, On rational surfaces, II, Mem. Coll. Sci. Univ. Kyoto, Ser. A., XXXIII (No. 2, 1960).
A. Neumaier, Lattices of simplex type, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 145--160. The sequence is on page 153.
EXAMPLE
G.f. = x + 3*x^2 + 6*x^3 + 10*x^4 + 16*x^5 + 27*x^6 + 56*x^7 + 240*x^8.
CROSSREFS
Sequence in context: A054886 A130578 A107068 * A038505 A369850 A119971
KEYWORD
fini,full,nonn
AUTHOR
N. J. A. Sloane, Feb 13 2002
STATUS
approved