|
Search: id:A055165
|
|
|
| A055165 |
|
Number of regular n X n matrices with rational entries equal to 0 or 1. |
|
+0
18
|
|
| 1, 6, 174, 22560, 12514320, 28836612000, 270345669985440, 10160459763342013440
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
All eigenvalues are nonzero.
|
|
REFERENCES
|
Miodrag Zivkovic, Classification of small (0,1) matrices, Linear Algebra and its Applications, 414 (2006), 310-346
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Miodrag Zivkovic, More information
Index entries for sequences related to binary matrices
|
|
FORMULA
|
For an asymptotic estimate see A046747. A002884 is a lower bound. A002416 is an upper bound.
a(n) = n! * A088389(n) - Gerald McGarvey (gerald.mcgarvey(AT)comcast.net), Oct 20 2007
|
|
EXAMPLE
|
For n=2 the 6 matrices are {{{0, 1}, {1, 0}}, {{0, 1}, {1, 1}}, {{1, 0}, {0, 1}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}, {{1, 1}, {1, 0}}}.
|
|
CROSSREFS
|
Cf. A056990, A056989, A046747, A055165, A002416, A003024 (positive definite matrices).
A046747(n) + a(n) = 2^(n^2) = total number of n X n (0, 1) matrices = sequence A002416.
Sequence in context: A003720 A002884 A166762 this_sequence A071095 A134632 A024277
Adjacent sequences: A055162 A055163 A055164 this_sequence A055166 A055167 A055168
|
|
KEYWORD
|
nonn,nice,hard
|
|
AUTHOR
|
Ulrich Hermisson (uhermiss(AT)server1.rz.uni-leipzig.de), Jun 18 2000
|
|
EXTENSIONS
|
More terms from MIodrag Zivkovic (ezivkovm(AT)matf.bg.ac.yu), Feb 28 2006
|
|
|
Search completed in 0.002 seconds
|
