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A103300 Number of perfect rulers with length n.

%I A103300 #61 Jan 03 2025 03:51:32
%S A103300 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 A103300 460,166,56,12,6,2036,890,304,120,20,10,2,2678,974,362,100,36,4,2,
%U A103300 4892,2114,684,238,68,22,4,16318,6350,2286,836,330,108,24,12,31980,12252
%N A103300 Number of perfect rulers with length n.
%C A103300 For definitions, references and links related to complete rulers see A103294.
%C A103300 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 A103300 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 A103300 From _Yannic Schröder_, Feb 22 2021: (Start)
%C A103300 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 A103300 A lower bound for 209 is 62, for 210 is 16, and for 211 is 204.
%C A103300 The verified value for 212 and for 213 is 4. (End)
%H A103300 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 A103300 Peter Luschny, <a href="http://luschny.de/math/rulers/rulercnt.html">Perfect and Optimal Rulers</a>.
%H A103300 Ed Pegg, <a href="https://community.wolfram.com/groups/-/m/t/2663076">Sparse ruler data</a>, Oct 20 2022.
%H A103300 Arch D. Robison, <a href="https://web.archive.org/web/20171111194139/http://software.intel.com/articles/parallel-computation-of-sparse-rulers">Parallel Computation of Sparse Rulers</a>, Jan 14 2014.
%H A103300 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 A103300 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 A103300 <a href="/index/Per#perul">Index entries for sequences related to perfect rulers.</a>
%F A103300 a(n) = T(n, A103298(n)) where the triangle T is described by A103294.
%e A103300 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 A103300 Cf. A004137 (Maximal number of edges in a graceful graph on n nodes).
%Y A103300 Cf. A103301, A103297, A103298.
%K A103300 hard,nonn,nice
%O A103300 0,4
%A A103300 _Peter Luschny_, Feb 28 2005