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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 (list; graph; refs; listen; history; text; internal format)
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'Angelo-Lebl) 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) 581-593.

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 Lebl-Lichtblau

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

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Last modified May 25 11:04 EDT 2019. Contains 323539 sequences. (Running on oeis4.)