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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.
1
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.
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 * A376911 A153460 A342209
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved