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%I #21 Feb 08 2022 14:24:01
%S 1,2,3,5,4,7,6,8,9,10,15,18,11,12,13,14,24,26,16,17,19,20,35,37,21,22,
%T 23,25,44,47,27,28,29,30,56,58,31,32,33,34,64,66,36,38,39,40,75,78,41,
%U 42,43,45,84,87,46,48,49,50,95,98,51,52,53,54,104,106,55,57,59,60,114,117,61,62,63,65,124,127,67
%N Concatenation of the lexicographically earliest 6-term closed circuits formed on a square grid by distinct segments of length a(n) at right angle.
%H Carole Dubois, <a href="/A351298/b351298.txt">Table of n, a(n) for n = 1..1002</a>
%H Eric Angelini, <a href="http://cinquantesignes.blogspot.com/2022/02/more-manhattan-distances.html">More Manhattan distinct distances</a>, Feb. 7th, 2022, personal blog.
%e [1, 2, 3, 5, 4, 7] is a closed circuit on a square grid formed by going 1 cell up (North), 2 cells to the right (East), 3 cells up again (North), 5 cells to the right again (East), 4 cells down (South) and 7 cells to the left (West); the next smallest such circuit is given by [6, 8, 9, 10, 15, 18] as all the terms of the final sequence must be distinct; the next circuit is [11, 12, 13, 14, 24, 26], etc. Concatenating all circuits gives the sequence.
%Y Cf. A101544 (where the array has 3 columns; there are 6 columns here: if we label them a, b, c, d, e, f the terms a + c = e and b + d = f).
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Feb 07 2022
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