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A210206 Maximal number of 1s in a Hadamard matrix of order 4n. 0


%S 12,42,90,160,240,344,462,598,756,922,1108,1314,1534,1772

%N Maximal number of 1s in a Hadamard matrix of order 4n.

%C The weight of a {-1,1} matrix is defined to be the number of elements equal to 1. The excess is defined to be the sum of the matrix elements. The weight and excess of an N x N matrix are related by (weight) = (excess + N^2) / 2. Hence a(n) = (A004118+16n^2)/2. - _William P. Orrick_, Jun 25 2015

%H Thomas A. Brown and Joel H. Spencer, <a href="http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.desklight-b216f85d-2474-4d76-802d-9d897db87f16?q=bwmeta1.element.desklight-ad25ec97-605c-4408-8b00-3da746f52675;25">Minimization of +-1 matrices under line shifts</a> Colloq. Math. 23 (1971), 165-171, 177 (errata).

%H N. Farmakis and S. Kounias, <a href="http://dx.doi.org/10.1016/0012-365X(87)90025-2">The excess of Hadamard matrices and optimal designs</a>, Discrete Mathematics, 67 (1987), 165-176.

%H S. Kounias and N. Farmakis, <a href="http://dx.doi.org/10.1016/0012-365X(88)90041-6">On the excess of Hadamard matrices</a>, Discrete Mathematics, 68 (1988), 59-69.

%H K. W. Schmidt, Edward T. H. Wang, <a href="http://dx.doi.org/10.1016/0097-3165(77)90017-6">The weights of Hadamard matrices</a>. J. Combinatorial Theory Ser. A 23 (1977), no. 3, 257--263. MR0453564 (56 #11826)

%H N. J. A. Sloane, <a href="http://neilsloane.com/hadamard/">Hadamard matrices</a>, gives representatives of all Hadamard matrix equivalence classes for sizes up to 28, and a representative of at least one equivalence class for sizes up to 256. Most are not of maximal weight, however.

%Y Cf. A004118.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Mar 18 2012

%E a(5)-a(14) from _William P. Orrick_, Jun 25 2015

%E Farmakis & Kounias references added by _William P. Orrick_, Jun 25 2015

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Last modified October 23 02:22 EDT 2018. Contains 316518 sequences. (Running on oeis4.)