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Number of distinct spans of length n with no 3-term arithmetic progression, containing zero, and with maximum element smallest possible.
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%I #21 Dec 20 2022 12:02:36

%S 1,1,2,1,4,7,6,1,2,2,2,1,2,2,20,1,14,2,2,2,4

%N Number of distinct spans of length n with no 3-term arithmetic progression, containing zero, and with maximum element smallest possible.

%C Offset by 1 from the same function in the referenced paper, which does not include zero in their count of how long spans are for the "well-spaced rows".

%H Noam Benson-Tilsen, Samuel Brock, Brandon Faunce, Monish Kumar, Noah Dokko Stein, and Joshua Zelinsky, <a href="https://arxiv.org/abs/2107.11706">Total Difference Labeling of Regular Infinite Graphs</a>, arXiv:2107.11706 [math.CO], 2021-2022.

%e a(5)=4 since we have as possible spans 0,1,3,7,8; 0,1,5,6,8; 0,1,5,7,8; 0,2,3,7,8. (It is easy to check that if the maximum term is 7 or lower then there must be fewer than 5 elements in the sequence.)

%Y Cf. A005047.

%K nonn,more

%O 1,3

%A _Joshua Zelinsky_, Nov 22 2022