0,2

This is the maximal value of the sum of the entries of any n X n Hadamard matrix (cf. A019442).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Best, M. R. The excess of a Hadamard matrix. Nederl. Akad. Wetensch. Proc. Ser. A {80}=Indag. Math. 39 (1977), no. 5, 357-361.

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

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. Farmakis and S. Kounias, The excess of Hadamard matrices and optimal designs, Discrete Mathematics, 67 (1987), 165-176. [From Will Orrick (worrick(AT)indiana.edu), Mar 26 2009]

S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Mathematics, 68 (1988), 59-69. [From Will Orrick (worrick(AT)indiana.edu), Mar 26 2009]

n^2*2^(-n)*binomial(n,n/2) <= a(n) <= n*sqrt(n).

Contribution from Will Orrick (worrick(AT)indiana.edu), 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<n/4<=4m^2+4m+1,

a(n/4)<=8[nm/4+1/2[n/4(n/4-1)/(2(m+1))]+(n-4)/8]+n+4, if 4m^2+4m+1<=n/4<4m^2+6m+3.

[x] denotes the integer part. (See Kounias and Farmakis, 1988.) (End)

Cf. A019442.

Sequence in context: A038522 A158865 A139570 this_sequence A082231 A073607 A086062

Adjacent sequences: A004115 A004116 A004117 this_sequence A004119 A004120 A004121

nonn,hard,more,nice

N. J. A. Sloane (njas(AT)research.att.com).

a(7) - a(14) from Will Orrick (worrick(AT)indiana.edu), Mar 26 2009