Sums of $k$-bonacci Numbers
arXiv:2208.012243 citations
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This is an incremental result for mathematicians interested in combinatorial identities and number sequences.
The paper provides a combinatorial proof of a formula for partial sums of k-bonacci numbers, expressed as alternating sums of powers of two times binomial coefficients, and derives a formula for the k-bonacci numbers themselves.
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.