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%I #54 May 30 2024 00:31:24
%S 2,1,2,1,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Number of Barker codes (or Barker sequences) of length n up to reversals and negations.
%C It is conjectured that there are no Barker codes of length > 13.
%C If there are any nonzero terms for n > 13, they are either at n = 3979201339721749133016171583224100 or at n larger than 4 * 10^33 (Borwein & Mossinghoff, 2014). - _Felix Fröhlich_, Feb 08 2017
%D R. H. Barker, Group synchronizing of binary digital sequences, in "Communication Theory", Butterworth, London, 1953, pp. 273-287.
%D H. D. Lueke, Korrelationssignale, Springer 1992.
%H Peter Borwein and Tamas Erdelyi, <a href="http://arxiv.org/abs/1206.5371">A note on Barker polynomials</a>, arXiv:1206.5371 [math.NT], 2012.
%H Peter Borwein and Michael J. Mossinghoff, <a href="https://doi.org/10.1112/S1461157013000223">Wieferich pairs and Barker sequences, II</a>, LMS Journal of Computation and Mathematics, Vol. 17, No. 1 (2014), 24-32.
%H Shalom Eliahou, <a href="http://images.math.cnrs.fr/Connait-on-toutes-les-suites-de-Barker.html">Connaît-on toutes les suites de Barker ?</a>, Images des Mathématiques, CNRS, 2022. In French.
%H Luis H. Gallardo, <a href="https://doi.org/10.13140/RG.2.2.13865.81761">Ryser's Conjecture and Stochastic matrices</a>, Univ. Brest (France 2024). See p. 2.
%H Brooke Logan Ogrodnik and Michael J. Mossinghoff, <a href="https://www.researchgate.net/publication/281628524">Double Wieferich pairs and circulant Hadamard matrices</a>, ResearchGate, 2015.
%H Michael J. Mossinghoff, <a href="https://doi.org/10.1007/s10623-009-9301-3">Wieferich pairs and Barker sequences</a>, Designs, Codes and Cryptography, Vol. 53, No. 3 (2009), 149-163.
%H Kai-Uwe Schmidt and Jürgen Willms, <a href="https://doi.org/10.1007/s10623-015-0104-4">Barker sequences of odd length</a>, Des. Codes Cryptogr. Vol. 80, No. 2 (2016), 409-414.
%H R. Turyn and J. Storer, <a href="http://dx.doi.org/10.1090/S0002-9939-1961-0125026-2">On binary sequences</a>, Proceedings of the American Mathematical Society, vol. 12, no. 3, pp. 394-399, 1961.
%H Jürgen Willms, <a href="http://arxiv.org/abs/1404.4833">Counterexamples to Theorem 1 of Turyn's and Storer's paper "On Binary Sequences"</a>, arXiv:1404.4833 [math.NT], 2014.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarkerCode.html">Barker Code</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Barker_code">Barker code</a>.
%e {{+, +}, {+, -}},
%e {{+, +, -}},
%e {{+, +, +, -}, {+, +, -, +}},
%e {{+, +, +, -, +}},
%e {{+, +, +, -, -, +, -}},
%e {{+, +, +, -, -, -, +, -, -, +, -}},
%e {{+, +, +, +, +, -, -, +, +, -, +, -, +}}
%Y Cf. A011758, A011759, A276690.
%K nonn
%O 2,1
%A _Eric W. Weisstein_, Jan 30 2004
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