

A003433


Hadamard maximal determinant problem: largest determinant of (+1,1)matrix of order n.
(Formerly M1291)


10



1, 2, 4, 16, 48, 160, 576, 4096, 14336, 73728, 327680, 2985984, 14929920, 77635584, 418037760, 4294967296, 21474836480, 146028888064, 894426939392, 10240000000000, 59392000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


REFERENCES

Ed Hughes and Rob Pratt, New Features in SAS/OR 13.1, SAS Paper SAS2562014; file:///Users/njasloane/Downloads/SAS256_Hughes_FinalPaper.pdf
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 formulae.


LINKS

Table of n, a(n) for n=1..21.
Richard P. Brent and Judyanne H. Osborn, On minors of maximal determinant matrices, Arxiv preprint arXiv:1208.3819, 2012.
W. P. Orrick and B. Solomon, Largedeterminant sign matrices of order 4k+1, Discr. Math. 307 (2007), 226236.
Eric Weisstein's World of Mathematics, 11Matrix
Index entries for sequences related to binary matrices
Index entries for sequences related to Hadamard matrices
Index entries for sequences related to maximal determinants


FORMULA

a(n) = 2^(n1)*A003432(n1). E.g., a(6) = 32*A003432(5) = 32*5 = 160.
a(n) <= n^(n/2).


CROSSREFS

A003432 is the main entry for this sequence.
Cf. A051753.
Cf. A188895 (number of distinct matrices having this maximal determinant).
Sequence in context: A119000 A034917 A215724 * A153951 A165905 A104354
Adjacent sequences: A003430 A003431 A003432 * A003434 A003435 A003436


KEYWORD

nonn,hard,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

Added a(19)a(21).
Edited by William P. Orrick, Dec 20 2011


STATUS

approved



