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A143108 Let H(2,d) be the space of polynomials p(x,y) of two variables with nonnegative coefficients such that p(x,y)=1 whenever x + y = 1. a(n) is the number of different polynomials in H(2,d) with exactly n distinct monomials and of maximum degree minus 1, i.e., of degree 2n-4. 2

%I

%S 0,0,3,4,10,24,32,56

%N Let H(2,d) be the space of polynomials p(x,y) of two variables with nonnegative coefficients such that p(x,y)=1 whenever x + y = 1. a(n) is the number of different polynomials in H(2,d) with exactly n distinct monomials and of maximum degree minus 1, i.e., of degree 2n-4.

%H J. P. D'Angelo, Simon Kos and Emily Riehl, <a href="http://dx.doi.org/10.1007/BF02921879">A sharp bound for the degree of proper monomial mappings between balls</a>, J. Geom. Anal., 13(4):581-593, 2003.

%H J. P. D'Angelo and J. Lebl, <a href="http://arXiv.org/abs/0708.3232">Complexity results for CR mappings between spheres</a>, arXiv:0708.3232 [math.CV], 2008.

%H J. P. D'Angelo and J. Lebl, <a href="http://dx.doi.org/10.1142/S0129167X09005248">Complexity results for CR mappings between spheres</a>, Internat. J. Math. 20 (2009), no. 2, 149-166.

%H J. Lebl and D. Lichtblau, <a href="http://arxiv.org/abs/0808.0284">Uniqueness of certain polynomials constant on a hyperplane</a>, arXiv:0808.0284 [math.CV], 2008-2010.

%H J. Lebl and D. Lichtblau, <a href="http://dx.doi.org/10.1016/j.laa.2010.04.020">Uniqueness of certain polynomials constant on a hyperplane</a>, Linear Algebra Appl., 433 (2010), no. 4, 824-837

%F Possibly can be computed from A143107 except for the third term, but this is not proved. Let b_n be elements of A143107, then a_n = 2 ( b_2 b_{n-1} + b_3 b_{n-2} + ... + b_{n-1} b_2 ).

%t See the paper by Lebl-Lichtblau.

%Y Cf. A143107, A143109.

%K hard,nonn,more

%O 1,3

%A Jiri Lebl (jlebl(AT)math.uiuc.edu), Jul 25 2008

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Last modified November 14 12:43 EST 2019. Contains 329115 sequences. (Running on oeis4.)