Finite generating functions for the sum of digits sequence

Abstract

We derive some new finite sums involving the sequence $s_2\left(n\right),$ the sum of digits of the expansion of $n$ in base $2.$ These functions allow us to generalize some classical results obtained by Allouche, Shallit and others.

26 pages, new version with simplified formulas and some new results

Cited by in corpus (1)

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