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 A004118 Maximal excess of a Hadamard matrix of order 4n. (Formerly M4489) 3
 0, 8, 20, 36, 64, 80, 112, 140, 172, 216, 244, 280, 324, 364, 408 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the maximal value of the sum of the entries of any n X n Hadamard matrix (cf. A019442). REFERENCES Brown, Thomas A. and Spencer, Joel H., 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. [From William P. Orrick, Mar 26 2009] S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Mathematics, 68 (1988), 59-69. [From William P. Orrick, Mar 26 2009] Seberry, Jennifer and Yamada, Mieko; Hadamard matrices, sequences and block designs, in Dinitz and Stinson, eds., Contemporary design theory, pp. 431-560, Wiley-Intersci. Ser. Discrete Math. Optim., Wiley, New York, 1992. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS M. R. Best, The excess of a Hadamard matrix, Indagat. Mathem. (Proceedings) 80 (1977), no. 5., 357-361 FORMULA n^2*2^(-n)*binomial(n,n/2) <= a(n) <= n*sqrt(n). Contribution from William P. Orrick, Mar 26 2009: (Start) a(n/4) <= n(2m+1)+8[n/4(n/4-1)/(2(2m+1))], if 4m^2<=n/4<=4m^2+2m+1 or 4m^2+6m+3<=n/4<=4(m+1)^2, a(n/4) <= 8[nm/4+1/2[n/4(n/4-1)/(2m)]-(n+4)/8]+n+4, if 4m^2+2m+1

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Last modified October 16 03:15 EDT 2019. Contains 328038 sequences. (Running on oeis4.)