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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A382605 Number of distinct solutions to the problem of folding in half a chain of linked rods of length 1, ..., n.

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%I A382605 #11 Apr 06 2025 19:48:29
%S A382605 0,0,1,1,0,0,1,2,0,0,1,1,0,0,2,1,0,0,1,3,0,0,1,2,0,0,3,1,0,0,1,2,0,0,
%T A382605 4,1,0,0,4,1,0,0,1,4,0,0,1,2,0,0,3,1,0,0,3,3,0,0,1,1,0,0,2,1,0,0,1,3,
%U A382605 0,0,1,1,0,0,4,1,0,0,1,4,0,0,1,5,0,0,3,1,0,0,1,3,0,0,2,1,0,0,6,1
%N A382605 Number of distinct solutions to the problem of folding in half a chain of linked rods of length 1, ..., n.
%C A382605 In order to be able to fold such chain in half, the total length of the chain (A000217(n)) has to be even, which is true when n=3 (mod 4) or n=0 (mod 4).
%C A382605 Conjecture: Whenever the length of the chain is even, there is at least one solution. That makes A154708 the sequence that lists numbers k that have at least one solution.
%H A382605 Daniel Mondot, <a href="/A382605/b382605.txt">Table of n, a(n) for n = 1..10000</a>
%H A382605 Allan Gottlieb, <a href="https://cs.nyu.edu/~gottlieb/tr/back-issues/2000s/2003/5-dec.pdf">Puzzle Corner</a>, Technology Review, December 2, 2003.
%e A382605 A chain of 7 rods of length 1 to 7, can be folded in half in only one way: 2+3+4+5 on one side, 6+7+1, on the other, both sides being 14 in total length. Therefore a(7) = 1.
%Y A382605 Cf. A380868, A382268, A380867, A382632.
%K A382605 nonn
%O A382605 1,8
%A A382605 _Daniel Mondot_, Mar 31 2025