Journal of Integer Sequences, Vol. 16 (2013), Article 13.3.7

Distribution of Values of the Binomial Coefficients and the Stern Sequence

Jennifer Lansing
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green St.
Urbana, IL 61801


The distribution of values in a sequence, as seen in counting the number of terms larger than a scalar times the average value, is applied to the the Stern sequence and the binomial coefficients. We also show that the suitably scaled logarithms of $\{ \binom{n} {k} : 0 \le k \le n \}$ converges to a distribution, and prove an implicit formula for the convergent function. We leave an open problem regarding the distribution of the Stern sequence.

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(Concerned with sequences A002487 A007318.)

Received September 18 2012; revised version received January 25 2013; February 22 2013. Published in Journal of Integer Sequences, March 2 2013.

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