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 A325683 #17 Feb 16 2025 08:33:58
%S A325683 1,1,1,2,2,4,2,6,8,18,16,24,20,28,42,76,100,138,168,204,194,272,276,
%T A325683 450,588,808,992,1578,1612,1998,2166,2680,2732,3834,3910,5716,6818,
%U A325683 9450,10524,15504,16640,22268,23754,30430,31498,40644,40294,52442,56344,72972,77184
%N A325683 Number of maximal Golomb rulers of length n.
%C A325683 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 up to sign.
%C A325683 Also the number of minimal (most refined) compositions of n such that every restriction to a subinterval has a different sum.
%H A325683 Fausto A. C. Cariboni, <a href="/A325683/b325683.txt">Table of n, a(n) for n = 0..100</a>
%H A325683 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler.</a>
%e A325683 The a(1) = 1 through a(8) = 8 maximal Golomb rulers:
%e A325683 {0,1} {0,2} {0,1,3} {0,1,4} {0,1,5} {0,1,4,6} {0,1,3,7} {0,1,3,8}
%e A325683 {0,2,3} {0,3,4} {0,2,5} {0,2,5,6} {0,1,5,7} {0,1,5,8}
%e A325683 {0,3,5} {0,2,3,7} {0,1,6,8}
%e A325683 {0,4,5} {0,2,6,7} {0,2,3,8}
%e A325683 {0,4,5,7} {0,2,7,8}
%e A325683 {0,4,6,7} {0,3,7,8}
%e A325683 {0,5,6,8}
%e A325683 {0,5,7,8}
%e A325683 The a(1) = 1 through a(10) = 16 minimal compositions:
%e A325683 (1) (2) (12) (13) (14) (132) (124) (125) (126) (127)
%e A325683 (21) (31) (23) (231) (142) (143) (135) (136)
%e A325683 (32) (214) (152) (153) (154)
%e A325683 (41) (241) (215) (162) (163)
%e A325683 (412) (251) (216) (172)
%e A325683 (421) (341) (234) (217)
%e A325683 (512) (243) (253)
%e A325683 (521) (261) (271)
%e A325683 (315) (316)
%e A325683 (324) (352)
%e A325683 (342) (361)
%e A325683 (351) (451)
%e A325683 (423) (613)
%e A325683 (432) (631)
%e A325683 (513) (712)
%e A325683 (531) (721)
%e A325683 (612)
%e A325683 (621)
%t A325683 fasmax[y_]:=Complement[y,Union@@(Most[Subsets[#]]&/@y)];
%t A325683 Table[Length[fasmax[Accumulate/@Select[Join@@Permutations/@IntegerPartitions[n],UnsameQ@@ReplaceList[#,{___,s__,___}:>Plus[s]]&]]],{n,0,15}]
%Y A325683 Rightmost column of A325677.
%Y A325683 Cf. A000079, A103295, A108917, A143823, A169942, A276024.
%Y A325683 Cf. A325676, A325678, A325679, A325681, A325687.
%K A325683 nonn
%O A325683 0,4
%A A325683 _Gus Wiseman_, May 13 2019
%E A325683 a(21)-a(50) from _Fausto A. C. Cariboni_, Feb 22 2022