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%I A033541 #16 Oct 29 2018 11:39:15
%S A033541 0,1,3,6,10,16,27,56,240
%N A033541 Number of irreducible exceptional curves of first kind on del Pezzo surface of degree 9-n.
%C A033541 The case n=1 is exceptional and a(1) could be 0 or 1.
%C A033541 a(n) is the number of vertices of the uniform (n-4)_21 polytope. - _Andrey Zabolotskiy_, Oct 29 2018
%D A033541 Yu. I. Manin, Rational surfaces and Galois cohomology, pp. 495-509 of Proc. International Congress Mathematicians, Moscow 1966.
%D A033541 Yu. I. Manin, Cubic Forms, Second edition, North-Holland Publishing Co., Amsterdam, 1986, page 136, Theorem 26.2(iii), Table (IV.9).
%H A033541 M. Nagata, <a href="https://doi.org/10.1215/kjm/1250776405">On rational surfaces, I</a>, Mem. Coll. Sci. Univ. Kyoto, Ser. A., XXXII (No. 3, 1960).
%H A033541 M. Nagata, <a href="https://doi.org/10.1215/kjm/1250775912">On rational surfaces, II</a>, Mem. Coll. Sci. Univ. Kyoto, Ser. A., XXXIII (No. 2, 1960).
%H A033541 A. Neumaier, <a href="http://dx.doi.org/10.1137/0604017">Lattices of simplex type</a>, SIAM J. Algebraic Discrete Methods 4 (1983), no. 2, 145--160. The sequence is on page 153.
%H A033541 Wikipedia, <a href="https://en.wikipedia.org/wiki/Uniform_k_21_polytope">Uniform k_21 polytope</a>
%e A033541 G.f. = x + 3*x^2 + 6*x^3 + 10*x^4 + 16*x^5 + 27*x^6 + 56*x^7 + 240*x^8.
%K A033541 fini,full,nonn
%O A033541 0,3
%A A033541 _N. J. A. Sloane_, Feb 13 2002

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