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.
%I A036501 #23 Feb 16 2025 08:32:37
%S A036501 1,1,1,2,4,5,1,1,1,2,1,1,1,1,1,1,1,1
%N A036501 Number of inequivalent Golomb rulers with n marks and shortest length.
%C A036501 From _Gus Wiseman_, May 31 2019: (Start)
%C A036501 A Golomb ruler of length n is a subset of {0..n} containing 0 and n and such that every pair of distinct terms has a different difference. For example, the a(2) = 1 through a(8) = 1 Golomb rulers are:
%C A036501 2: {0,1}
%C A036501 3: {0,1,3}
%C A036501 4: {0,1,4,6}
%C A036501 5: {0,1,4,9,11}
%C A036501 5: {0,2,7,8,11}
%C A036501 6: {0,1,4,10,12,17}
%C A036501 6: {0,1,4,10,15,17}
%C A036501 6: {0,1,8,11,13,17}
%C A036501 6: {0,1,8,12,14,17}
%C A036501 7: {0,1,4,10,18,23,25}
%C A036501 7: {0,1,7,11,20,23,25}
%C A036501 7: {0,2,3,10,16,21,25}
%C A036501 7: {0,2,7,13,21,22,25}
%C A036501 7: {0,1,11,16,19,23,25}
%C A036501 8: {0,1,4,9,15,22,32,34}
%C A036501 Also half the number of length-(n - 1) compositions of A003022(n) such that every consecutive subsequence has a different sum. For example, the a(2) = 1 through a(8) = 1 compositions are (A = 10):
%C A036501 2: (1)
%C A036501 3: (1,2)
%C A036501 4: (1,3,2)
%C A036501 5: (1,3,5,2)
%C A036501 5: (2,5,1,3)
%C A036501 6: (1,3,6,2,5)
%C A036501 6: (1,3,6,5,2)
%C A036501 6: (1,7,3,2,4)
%C A036501 6: (1,7,4,2,3)
%C A036501 7: (1,3,6,8,5,2)
%C A036501 7: (1,6,4,9,3,2)
%C A036501 7: (2,1,7,6,5,4)
%C A036501 7: (2,5,6,8,1,3)
%C A036501 7: (1,A,5,3,4,2)
%C A036501 8: (1,3,5,6,7,A,2)
%C A036501 (End)
%H A036501 Anonymous, <a href="http://members.aol.com/golomb20">In Search Of The Optimal 20, 21 and 22 Mark Golomb Rulers</a>
%H A036501 Distributed.Net, <a href="http://www.distributed.net/ogr">Project OGR</a>
%H A036501 J. B. Shearer, <a href="http://www.research.ibm.com/people/s/shearer/gropt.html">Table of known optimal Golomb rulers</a>
%H A036501 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler</a>
%H A036501 <a href="/index/Go#Golomb">Index entries for sequences related to Golomb rulers</a>
%Y A036501 Cf. A003022, A039953, A054578, A108917, A143823, A169942, A270813, A325677, A325683.
%K A036501 nonn,hard,nice,more
%O A036501 2,4
%A A036501 _N. J. A. Sloane_