Non-standard decompositions explore Fibonacci sums in number theory, revealing new recurrence relations.
We study B(n;k), the number of ways of writing n as a sum or difference of the first k Fibonacci numbers. We show that B(0;k) satisfies the Tribonacci-like recurrence B(0;k+1)=B(0;k)+B(0;k−1)+B(0;k−2) and that B(n;k) satisfies a modified version of this recurrence.
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Anders et al. (2026) studied this question.
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