Combinatorial sums and finite differences
نویسندگان
چکیده
منابع مشابه
Combinatorial sums and finite differences
We present a new approach to evaluating combinatorial sums by using finite differences. Let {ak}k=0 and {bk}k=0 be sequences with the property that ∆bk = ak for k ≥ 0. Let gn = ∑n k=0 ( n k ) ak, and let hn = ∑n k=0 ( n k ) bk. We derive expressions for gn in terms of hn and for hn in terms of gn. We then extend our approach to handle binomial sums of the form ∑n k=0 ( n k ) (−1)ak, ∑ k ( n 2k ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.03.052