%I #51 Feb 24 2021 09:09:45

%S 1,1,1,2,3,4,2,12,8,4,38,30,14,6,130,80,32,12,500,326,150,66,18,4,944,

%T 460,166,56,12,6,2036,890,304,120,20,10,2,2678,974,362,100,36,4,2,

%U 4892,2114,684,238,68,22,4,16318,6350,2286,836,330,108,24,12,31980,12252

%N Number of perfect rulers with length n.

%C For definitions, references and links related to complete rulers see A103294.

%C The values for n = 208-213 are 22,0,0,0,4,4 according to Arch D. Robison. The values for 199-207 are not yet known. - _Peter Luschny_, Feb 20 2014, Jun 28 2019

%C Zero values at 135, 136, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196, 209, 210, 211. - _Ed Pegg Jr_, Jun 23 2019 [These values were found by Arch D. Robison, see links. _Peter Luschny_, Jun 28 2019]

%C From _Yannic Schröder_, Feb 22 2021: (Start)

%C Zero values at 135, 136, 149, 150, 151, 164, 165, 166, 179, 180, 181, 195, 196 have been replaced with correct values using an additional mark.

%C A lower bound for 209 is 62, for 210 is 16, and for 211 is 204.

%C The verified value for 212 and for 213 is 4. (End)

%H Peter Luschny (0..123), Arch D. Robison (124..198) and Fabian Schwartau and Yannic Schröder (199..208), <a href="/A103300/b103300.txt">Table of n, a(n) for n = 0..208</a>

%H Peter Luschny, <a href="http://luschny.de/math/rulers/rulercnt.html">Perfect and Optimal Rulers.

%H Arch D. Robison, <a href="http://software.intel.com/articles/parallel-computation-of-sparse-rulers">Parallel Computation of Sparse Rulers</a>, Jan 14 2014.

%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="https://dx.doi.org/10.21227/cd4b-nb07">MRLA search results and source code</a>, Nov 6 2020.

%H F. Schwartau, Y. Schröder, L. Wolf and J. Schoebel, <a href="https://doi.org/10.1109/OJAP.2020.3043541">Large Minimum Redundancy Linear Arrays: Systematic Search of Perfect and Optimal Rulers Exploiting Parallel Processing</a>, IEEE Open Journal of Antennas and Propagation, 2 (2021), 79-85.

%H <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>

%F a(n) = T(n, A103298(n)) where the triangle T is described by A103294.

%e a(5)=4 counts the perfect rulers with length 5, {[0,1,3,5],[0,2,4,5],[0,1,2,5],[0,3,4,5]}.

%Y Cf. A004137 (Maximal number of edges in a graceful graph on n nodes).

%Y Cf. A103301, A103297, A103298.

%K hard,nonn,nice

%O 0,4

%A _Peter Luschny_, Feb 28 2005