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On indefinite sums weighted by periodic sequences (1804.06418v2)
Published 17 Apr 2018 in math.CO, cs.DM, and math.NT
Abstract: For any integer $q\geq 2$ we provide a formula to express indefinite sums of a sequence $(f(n)){n\geq 0}$ weighted by $q$-periodic sequences in terms of indefinite sums of sequences $(f(qn+p)){n\geq 0}$, where $p\in{0,\ldots,q-1}$. When explicit expressions for the latter sums are available, this formula immediately provides explicit expressions for the former sums. We also illustrate this formula through some examples.