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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 (list; constant; graph; refs; listen; history; text; internal format)
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, ANTS-I Ithaca, NY, USA, May 6-9, 1994, Proceedings, Lecture Notes in Computer Science, Vol. 877, Springer, Berlin, Heidelberg, 1994, pp. 144-158; Inria preprint.

Hervé Daudé, Philippe Flajolet and Brigitte Vallée, An average-case analysis of the Gaussian algorithm for lattice reduction, Combinatorics, Probability and computing, Vol. 6, No. 4 (1997), pp. 397-433; 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

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Last modified December 5 09:45 EST 2021. Contains 349543 sequences. (Running on oeis4.)