The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A074664

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A074664

Number of algebraically independent elements of degree n in the algebra of symmetric polynomials in noncommuting variables.
(history; published version)

#154 by Michel Marcus at Sun Feb 13 04:34:28 EST 2022

STATUS

reviewed

approved

#153 by Joerg Arndt at Sun Feb 13 04:31:28 EST 2022

STATUS

proposed

reviewed

#152 by Jon E. Schoenfield at Sun Feb 13 04:27:32 EST 2022

STATUS

editing

proposed

#151 by Jon E. Schoenfield at Sun Feb 13 04:27:23 EST 2022

FORMULA

G.f.: (of 1,1,2,6,.. .) 1/(1-x-x^2/(1-3x-2x^2/(1-4x-3x^2/(1-5x-4x^2/(1-6x-5x^2/(1-... (continued fraction);

From Sergei N. Gladkovskii, Sep 28 2012 to May 19 2013: (Start) Continued fractions:

Continued fractions:

G.f.: (2+(x^2-4)/(U(0)-x^2+4))/x where U(k) = k*(2*k+3)*x^2 + x - 2 - (2 - x + 2*k*x)*(2 + 3*x + 2*k*x)*(k+1)*x^2/U(k+1).

G.f.: (1+U(0))/x where U(k) = +x*k - 1 + x - x^2*(k+1)/U(k+1).

G.f.: 1 + 1/x - U(0)/x where U(k) = 1 + x - x*(k+1)/(1 - x/U(k+1)).

G.f.: 1/x - ((1+x)/x)/G(0) where G(k) = 1 - 2*x*(k+1)/((2*k+1)*(2*x*k-1) - x*(2*k+1)*(2*k+3)*(2*x*k-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+x-1)/G(k+1))).

G.f.: Q(0) where Q(k) = 1 + x/(1 - x + x*(k+1)/(x - 1/Q(k+1))). (End)

STATUS

approved

editing

#150 by N. J. A. Sloane at Tue Feb 25 21:46:04 EST 2020

STATUS

proposed

approved

#149 by Michael De Vlieger at Tue Feb 25 20:52:06 EST 2020

STATUS

editing

proposed

#148 by Michael De Vlieger at Tue Feb 25 20:52:04 EST 2020

LINKS

Chunyan Yan, Zhicong Lin, <a href="https://arxiv.org/abs/1912.03674">Inversion sequences avoiding pairs of patterns</a>, arXiv:1912.03674 [math.CO], 2019.

STATUS

approved

editing

#147 by Georg Fischer at Thu Jan 03 13:45:05 EST 2019

STATUS

editing

approved

#146 by Georg Fischer at Thu Jan 03 13:44:57 EST 2019

LINKS

Marcelo Aguiar and Swapneel Mahajan, <a href="http://mosaicpi.math.tamucornell.edu/~maguiar/hadamard.pdf">On the Hadamard product of Hopf monoids</a>

M. Meng He, J. Ian Munro, S. Srinivasa Rao, <a href="httphttps://wwwweb.cs.uwaterloodal.ca/~mhe/research/conferencepublications/soda05_suffixarray.pdf">A Categorization Theorem on Suffix Arrays with Applications to Space Efficient Text Indexes</a>, SODA 2005, Definition 2.2.

STATUS

approved

editing

#145 by OEIS Server at Wed Jan 02 10:31:14 EST 2019

LINKS

Vaclav Kotesovec, <a href="/A074664/b074664_1.txt">Table of n, a(n) for n = 1..573</a> (terms 1..100 from T. D. Noe)