A033541 Number of irreducible exceptional curves of first kind on del Pezzo surface of degree 9-n.

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

Table of n, a(n) for n=0..8.

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.

Wikipedia, Uniform k_21 polytope

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

Adjacent sequences: A033538 A033539 A033540 * A033542 A033543 A033544

Keyword

fini,full,nonn

Author

N. J. A. Sloane, Feb 13 2002

Status

approved