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%I #63 Apr 12 2022 06:37:49
%S 1,1,1,3,4,9,17,33,63,128,248,495,988,1969,3911,7857,15635,31304,
%T 62732,125501,250793,503203,1006339,2014992,4035985,8080448,16169267,
%U 32397761,64826967,129774838,259822143,520063531,1040616486,2083345793,4168640894,8342197304,16694070805,33404706520,66832674546,133736345590
%N Number of complete rulers with length n.
%C For definitions, references and links related to complete rulers see A103294.
%C Also the number of compositions of n whose consecutive subsequence-sums cover an initial interval of the positive integers. For example, (2,3,1) is such a composition because (1), (2), (3), (3,1), (2,3), and (2,3,1) are subsequences with sums covering {1..6}. - _Gus Wiseman_, May 17 2019
%C a(n) ~ c*2^n, where 0.2427 < c < 0.2459. - _Fei Peng_, Oct 17 2019
%H Fausto A. C. Cariboni, <a href="/A103295/b103295.txt">Table of n, a(n) for n = 0..49</a>
%H Scott Harvey-Arnold, Steven J. Miller, and Fei Peng, <a href="https://arxiv.org/abs/2001.08931">Distribution of missing differences in diffsets</a>, arXiv:2001.08931 [math.CO], 2020.
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/PerfectRulers">Perfect rulers</a>
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a103295.txt">Count complete rulers of given length.</a> FORTRAN program.
%H <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>
%H Gus Wiseman, <a href="/A103295/a103295.txt">Illustration of A103295</a>.
%F a(n) = Sum_{i=0..n} A103294(n, i) = Sum_{i=A103298(n)..n} A103294(n, i).
%e a(4) = 4 counts the complete rulers with length 4, {[0,2,3,4],[0,1,3,4],[0,1,2,4],[0,1,2,3,4]}.
%t Table[Length[Select[Join@@Permutations/@IntegerPartitions[n],SubsetQ[ReplaceList[#,{___,s__,___}:>Plus[s]],Range[n]]&]],{n,0,15}] (* _Gus Wiseman_, May 17 2019 *)
%Y Cf. A103300 (Perfect rulers with length n). Main diagonal of A349976.
%Y Cf. A000079, A126796, A143823, A169942, A325676, A325677, A325683, A325684, A325685.
%K nonn
%O 0,4
%A _Peter Luschny_, Feb 28 2005
%E a(30)-a(36) from _Hugo Pfoertner_, Mar 17 2005
%E a(37)-a(38) from _Hugo Pfoertner_, Dec 10 2021
%E a(39) from _Hugo Pfoertner_, Dec 16 2021
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