A245253 Decimal expansion of d_0, the constant term in the asymptotic expansion of the average number of registers needed to evaluate a binary tree.

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

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 311.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Helmut Prodinger, Philippe Flajolet and the Register function

Helmut Prodinger, Introduction to Philippe Flajolet’s work on the Register function.

Formula

d_0 = 1/2 - gamma/(2*log(2)) - 1/log(2) + log(Pi)/log(2), where gamma is Euler's constant (gamma ~ 0.577216).

Example

0.29242799994492181536014585440205743001061520709689154445559...

Mathematica

d0 = 1/2 - EulerGamma/(2*Log[2]) - 1/Log[2] + Log[2, Pi]; RealDigits[d0, 10, 103] // First

Prog

(PARI) default(realprecision, 100); 1/2 - Euler/(2*log(2)) - 1/log(2) + log(Pi)/log(2)  \\ G. C. Greubel, Sep 06 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 1/2 - EulerGamma(R)/(2*Log(2)) - 1/Log(2) + Log(Pi(R))/Log(2); // G. C. Greubel, Sep 06 2018

Crossrefs

Cf. A001620.

Sequence in context: A021346 A281334 A010597 * A153460 A342209 A248695

Adjacent sequences: A245250 A245251 A245252 * A245254 A245255 A245256

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 15 2014

Status

approved