

A143105


Let g_0(x,y)=x, g_1(x,y)=x^3+3xy and g_{n+2}(x,y) = (x^2+2y)g_{n+1}(x+y)y^2g_n(x,y). The entries of the sequence are those odd d for which g_d(x,y) and cx^jy^kg_m(x,y) have at least two terms in common (same coefficients) for some c > 0 and integers j,k and such that g_d(x,y) + cx^jy^k(1+y^m  g_m(x,y)) has all positive coefficients.


1



1, 3, 5, 9, 17, 21, 33, 41, 45, 53, 69, 77, 81, 93, 105, 113, 117, 125, 129, 141, 149, 153, 161, 165, 177, 185, 201, 213, 221, 225, 249, 261, 269, 273, 285, 297, 305, 309, 333, 341, 345, 357, 365, 369, 381, 405, 413, 417, 429, 437, 441, 453, 465, 473, 489, 501
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OFFSET

0,2


COMMENTS

Note that g_k(x,y) always has positive coefficients. The sequence are degrees for which a certain construction (see paper by D'AngeloLebl) of proper monomial holomorphic mappings of balls does not give new noninvariant monomial mappings.
It is unknown if this sequence is infinite (conjectured to be so). Furthermore A143106 is definitely a subsequence of this sequence, but it is unknown if the two are in fact equal.


REFERENCES

J. P. D'Angelo, Simon Kos and Emily Riehl. A sharp bound for the degree of proper monomial mappings between balls. J. Geom. Anal., 13(4) (2003) 581593.


LINKS

Table of n, a(n) for n=0..55.
J. P. D'Angelo and J. Lebl. Complexity results for CR mappings between spheres, arXiv:0708.3232, Internat. J. Math. 20 (2) (2009) 149
J. Lebl and D. Lichtblau, Uniqueness of certain polynomials constant on a hyperplane, arXiv:0808.0284 (2008).


EXAMPLE

For example when d=7, we get the following new polynomials x^7 + 7/2 xy + 7/2 x^5y 7/2 xy^5 and x^7 + 7 x^3y + 7 xy^3 + 7 x^3y^3. Hence 7 is not in the sequence.


MATHEMATICA

See the paper by LeblLichtblau


CROSSREFS

Cf. A143106.
Sequence in context: A217099 A276970 A294641 * A032679 A154607 A287207
Adjacent sequences: A143102 A143103 A143104 * A143106 A143107 A143108


KEYWORD

nonn


AUTHOR

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


STATUS

approved



