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A039953 Triangle of "canonical" optimal Golomb rulers.

%I A039953 #28 Feb 16 2025 08:32:38
%S A039953 1,1,2,1,3,2,1,3,5,2,1,3,6,2,5,1,3,6,8,5,2,1,3,5,6,7,10,2,1,4,7,13,2,
%T A039953 8,6,3,1,5,4,13,3,8,7,12,2,1,3,9,15,5,14,7,10,6,2,2,4,18,5,11,3,12,13,
%U A039953 7,1,9,2,3,20,12,6,16,11,15,4,9,1,7
%N A039953 Triangle of "canonical" optimal Golomb rulers.
%C A039953 n-th row gives first differences of the (n+1)-th row of A106683. - _Andrey Zabolotskiy_, Aug 22 2017
%D A039953 CRC Handbook of Combinatorial Designs, 1996, p. 315.
%D A039953 A. Kotzig and P. J. Laufer, Sum triangles of natural numbers having minimum top, Ars. Combin. 21 (1986), 5-13.
%H A039953 Distributed.Net, <a href="http://www.distributed.net/ogr">Project OGR</a>
%H A039953 L. Miller, <a href="https://web.archive.org/web/20030404100258/http://www.cuug.ab.ca:80/~millerl/g3-records.html">Golomb Rulers</a>
%H A039953 B. Rankin, <a href="https://web.archive.org/web/20120418104127/http://people.ee.duke.edu:80/~wrankin/golomb/golomb.html">Golomb Ruler Calculations</a>
%H A039953 J. B. Shearer, <a href="http://www.research.ibm.com/people/s/shearer/grtab.html">Golomb ruler table</a>
%H A039953 N. J. A. Sloane, <a href="/A003022/a003022.gif">First few optimal Golomb rulers</a>
%H A039953 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler</a>
%H A039953 Wikipedia, <a href="https://en.wikipedia.org/wiki/Golomb_ruler">Golomb ruler</a>
%H A039953 <a href="/index/Go#Golomb">Index entries for sequences related to Golomb rulers</a>
%e A039953 Triangle begins:
%e A039953   1;
%e A039953   1, 2;
%e A039953   1, 3, 2;
%e A039953   1, 3, 5, 2;
%e A039953   1, 3, 6, 2, 5;
%e A039953   1, 3, 6, 8, 5, 2;
%e A039953   ...
%Y A039953 Cf. A003022, A036501.
%Y A039953 These all start at 1. For rulers starting at 0, see A079283, A079287, A079423, A079425, A079426, A079430, A079433, A079434, A079435, A079454 and A079467, A079604, A079605, A079606, A079607, A079608, A079625, A079634.
%K A039953 nonn,tabl,nice
%O A039953 1,3
%A A039953 _N. J. A. Sloane_
%E A039953 Corrected by _Philip Newton_, Feb 06 2002
%E A039953 Corrected by _Andrey Zabolotskiy_, Aug 22 2017