A195600 - OEIS

A195600

Continued fraction for beta = 3/(2*log(alpha/2)); alpha = A195596.

1, 1, 20, 3, 2, 7, 1, 1, 1, 12, 1, 5, 1, 91, 1, 1, 3, 87, 2, 1, 1, 1, 1, 3, 1, 9, 3, 2, 1, 1, 1, 1, 190, 1, 3, 1, 82, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 2, 12, 6, 2, 2, 2, 3, 2, 1, 1, 1, 2, 3, 21, 1, 1, 12, 1, 7, 3, 2, 26, 3, 2, 1, 1, 1, 9, 1, 15, 4, 3, 3, 1, 3, 1

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OFFSET

0,3

COMMENTS

beta is used to measure the expected height of random binary search trees.

LINKS

Table of n, a(n) for n=0..82.

B. Reed, The height of a random binary search tree, J. ACM, 50 (2003), 306-332.

FORMULA

beta = 3/(2*log(alpha/2)) = 3*alpha/(2*alpha-2), where alpha = A195596 = -1/W(-exp(-1)/2) and W is the Lambert W function.

A195582(n)/A195583(n) = alpha*log(n) - beta*log(log(n)) + O(1).

EXAMPLE