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a(n) is the smallest positive integer which can be represented as the sum of distinct positive Fibonacci n-step numbers (with a single type of 1) in exactly n ways, or -1 if no such integer exists.
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%I #20 Feb 16 2025 08:34:04

%S 1,3,44,416,26815,464031

%N a(n) is the smallest positive integer which can be represented as the sum of distinct positive Fibonacci n-step numbers (with a single type of 1) in exactly n ways, or -1 if no such integer exists.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>

%e For n = 2: 3 = Fibonacci(4) = 3 = Fibonacci(2) + Fibonacci(3) = 1 + 2.

%Y Cf. A000119, A013583, A117546, A287656, A288120.

%K nonn,more,changed

%O 1,2

%A _Ilya Gutkovskiy_, Jan 08 2023