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A210206 Maximal number of 1s in a Hadamard matrix of order 4n. 0
12, 42, 90, 160, 240, 344, 462, 598, 756, 922, 1108, 1314, 1534, 1772 (list; graph; refs; listen; history; text; internal format)



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


Table of n, a(n) for n=1..14.

Thomas A. Brown and Joel H. Spencer, Minimization of +-1 matrices under line shifts Colloq. Math. 23 (1971), 165-171, 177 (errata).

N. Farmakis and S. Kounias, The excess of Hadamard matrices and optimal designs, Discrete Mathematics, 67 (1987), 165-176.

S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Mathematics, 68 (1988), 59-69.

K. W. Schmidt, Edward T. H. Wang, The weights of Hadamard matrices. J. Combinatorial Theory Ser. A 23 (1977), no. 3, 257--263. MR0453564 (56 #11826)

N. J. A. Sloane, Hadamard matrices, 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.


Cf. A004118.

Sequence in context: A270700 A282693 A045945 * A005901 A090554 A009948

Adjacent sequences:  A210203 A210204 A210205 * A210207 A210208 A210209




N. J. A. Sloane, Mar 18 2012


a(5)-a(14) from William P. Orrick, Jun 25 2015

Farmakis & Kounias references added by William P. Orrick, Jun 25 2015



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Last modified January 24 21:12 EST 2021. Contains 340411 sequences. (Running on oeis4.)