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Sums of $k$-bonacci Numbers

Published 2 Aug 2022 in math.CO and cs.DM | (2208.01224v1)

Abstract: We give a combinatorial proof of a formula giving the partial sums of the $k$-bonacci sequence as alternating sums of powers of two multiplied by binomial coefficients. As a corollary we obtain a formula for the $k$-bonacci numbers.

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