The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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)
 OFFSET 1,1 COMMENTS 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 LINKS 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. CROSSREFS Cf. A004118. Sequence in context: A270700 A282693 A045945 * A005901 A090554 A009948 Adjacent sequences:  A210203 A210204 A210205 * A210207 A210208 A210209 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Mar 18 2012 EXTENSIONS a(5)-a(14) from William P. Orrick, Jun 25 2015 Farmakis & Kounias references added by William P. Orrick, Jun 25 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 8 04:32 EDT 2020. Contains 336290 sequences. (Running on oeis4.)