A003433 - OEIS (original) (raw)

1, 2, 4, 16, 48, 160, 576, 4096, 14336, 73728, 327680, 2985984, 14929920, 77635584, 418037760, 4294967296, 21474836480, 146028888064, 894426939392, 10240000000000, 59392000000000, 409600000000000

COMMENTS

I added the entry for n=22 since this has been proved optimal by Chasiotis et al (reference in A003432). - Richard P. Brent, Aug 17 2021

REFERENCES

Ed Hughes and Rob Pratt, New Features in SAS/OR 13.1, SAS Paper SAS256-2014.

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

See A003432 for further references, links and formulas.

FORMULA

a(n) = 2^(n-1)*A003432(n-1). E.g., a(6) = 32*A003432(5) = 32*5 = 160.

a(n) <= n^(n/2).

MATHEMATICA

A003432 = Cases[Import["https://oeis.org/[A003432](/A003432 "Hadamard maximal determinant problem: largest determinant of a (real) {0,1}-matrix of order n.")/b003432.txt", "Table"], {_, _}][[All, 2]];

a[n_] := 2^(n-1) A003432[[n]];

CROSSREFS

A003432 is the main entry for this sequence.

Cf. A188895 (number of distinct matrices having this maximal determinant).