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A245250 Decimal expansion of the average value of the Yekutieli-Mandelbrot parameter, that is the average number of maximal subtrees of an ordered binary tree requiring one less register than the whole tree. 2

%I #11 Sep 08 2022 08:46:08

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

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

%U 8,5,9,6,5,2,3,3,5,1,6,3,2,3,3,4,2,4,4,4,1,9,7,2,4,3,7,1,4,6,7,3,5,7,2,5

%N Decimal expansion of the average value of the Yekutieli-Mandelbrot parameter, that is the average number of maximal subtrees of an ordered binary tree requiring one less register than the whole tree.

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

%H G. C. Greubel, <a href="/A245250/b245250.txt">Table of n, a(n) for n = 1..10000</a>

%H Helmut Prodinger, <a href="http://math.sun.ac.za/~hproding/abstract/abs_113.htm">On a problem of Yekutieli and Mandelbrot about the bifurcation ratio of binary trees</a>

%F 2*G/(Pi*log(2))+5/2, where G is Catalan's constant (G ~ 0.915966).

%e 3.341266940724730471889348860254734362026317624560016898783179693499...

%t RealDigits[2*Catalan/(Pi*Log[2])+5/2, 10, 104] // First

%o (PARI) default(realprecision, 100); 2*Catalan/(Pi*log(2))+5/2 \\ _G. C. Greubel_, Aug 25 2018

%o (Magma) SetDefaultRealField(RealField(100)); R:=RealField(); 2*Catalan(R)/(Pi(R)*Log(2))+5/2; // _G. C. Greubel_, Aug 25 2018

%Y Cf. A006752.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jul 15 2014

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)