

A074904


Decimal expansion of trace of Gaussian operator.


0



1, 4, 4, 4, 6, 2, 3, 9, 6, 2, 4, 6, 1, 6, 0, 8, 1, 5, 8, 8, 2, 4, 9, 9, 0, 9, 0, 5, 2, 5, 4, 8, 3, 2, 0, 3, 8, 1, 3, 6, 4, 2, 0, 7, 1, 9, 7, 8, 3, 0, 7, 7, 9, 1, 4, 9, 5, 8, 4, 3, 5, 0, 7, 4, 6, 0, 7, 4, 3, 5, 2, 9, 6, 4, 1, 5, 4, 6, 7, 3, 2, 0, 8, 1, 8, 1, 3
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OFFSET

0,2


REFERENCES

Marius Iosifescu, and Cor Kraaikamp, Metrical Theory of Continued Fractions, Springer, 2002, p. 134.


LINKS

Table of n, a(n) for n=0..86.
Hervé Daudé, Philippe Flajolet and Brigitte Vallée, An analysis of the Gaussian algorithm for lattice reduction, in: L. M. Adleman and M. D. Huang (eds.), Algorithmic Number Theory, First International Symposium, ANTSI Ithaca, NY, USA, May 69, 1994, Proceedings, Lecture Notes in Computer Science, Vol. 877, Springer, Berlin, Heidelberg, 1994, pp. 144158; Inria preprint.
Hervé Daudé, Philippe Flajolet and Brigitte Vallée, An averagecase analysis of the Gaussian algorithm for lattice reduction, Combinatorics, Probability and computing, Vol. 6, No. 4 (1997), pp. 397433; Inria preprint.


FORMULA

From Amiram Eldar, May 27 2021: (Start)
Equals Sum_{m>=1} 1/(tau(m)^4 + tau(m)^2), where tau(m) = (m + sqrt(m^2+4))/2.
Equals 7/2  7/(2*sqrt(2))  2/sqrt(5)  (1/2) * Sum_{k>=2} (1)^k * binomial(2*k,k)*(zeta(2*k)  1  1/2^(2*k))*(k  1)/(k + 1). (End)


EXAMPLE

0.14446239624616081588249909052548320381...


MATHEMATICA

RealDigits[7/2  7/(2 Sqrt[2])  2/Sqrt[5] + NSum[(1)^k * Binomial[2*k, k]*(Zeta[2*k]  1  1/2^(2*k))*(k  1)/(k + 1), {k, 1, Infinity}, Method > "AlternatingSigns", WorkingPrecision > 500]/2, 10, 100][[1]] (* Amiram Eldar, May 27 2021 *)


CROSSREFS

Sequence in context: A006075 A342576 A241295 * A010304 A164821 A348677
Adjacent sequences: A074901 A074902 A074903 * A074905 A074906 A074907


KEYWORD

nonn,cons


AUTHOR

N. J. A. Sloane, Sep 15 2002


EXTENSIONS

Offset corrected and more terms added by Amiram Eldar, May 27 2021


STATUS

approved



