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A085340 a(n) is the value of determinant of the following special matrix: diagonal values equal to n-2; upper triangular entries equal to -1; lower triangular values are +1. 2
-1, 1, 4, 41, 528, 8177, 148160, 3077713, 72147712, 1884629825, 54294967296, 1710428956601, 58496602689536, 2158563109641265, 85487558566199296, 3616912482448035233, 162819625954342010880, 7770488166051562690817, 391896604540625999888384 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

These invertible matrices are used in formal neural network theory to generate transient-free state transition graphs with using suitable threshold vectors.

REFERENCES

Labos E.: The most complicated networks of formal neurons. In Proc. of IEEE. first International Conference on Neural Networks. San Diego,USA,1987.[Editors: Caudill,M. and Butler Ch.]; Vol. III, pp. 301-308.

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

n=5: matrix =

+3,-1,-1,-1,-1

+1,+3,-1,-1,-1

+1,+1,+3,-1,-1

+1,+1,+1,+3,-1

+1,+1,+1,+1,+3,

with determinant=528=a(5). a(1)=-1 is the only negative term.

MATHEMATICA

f[x_, y_] := Sign[y-x] g[x_, y_, z_] := (z-2)*(1-Abs[f[x, y]]); a=Table[Table[f[w, s], {w, 1, q}], {s, 1, q}]; b=Table[Table[g[w, s, q], {w, 1, q}], {s, 1, q}]; m=matrix=a+b; Det[m]; Table[Det[Table[Table[f[w, s]+g[w, s, q], {w, 1, q}], {s, 1, q}]], {q, 1, 20}]

CROSSREFS

Sequence in context: A110041 A064327 A134277 * A230251 A001908 A270703

Adjacent sequences:  A085337 A085338 A085339 * A085341 A085342 A085343

KEYWORD

sign

AUTHOR

Labos Elemer, Jul 08 2003

STATUS

approved

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Last modified September 19 04:50 EDT 2020. Contains 337175 sequences. (Running on oeis4.)