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Search: id:A085340
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| A085340 |
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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. |
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+0
3
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| -1, 1, 4, 41, 528, 8177, 148160, 3077713, 72147712, 1884629825, 54294967296, 1710428956601, 58496602689536, 2158563109641265, 85487558566199296, 3616912482448035233, 162819625954342010880, 7770488166051562690817, 391896604540625999888384
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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These invertible matrices are used in formal neural network theory to generate transient-free state transition graphs with using suitable threshold vectors.
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REFERENCES
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Labos E.: The most complicated networks of formal neurons. In Proc. of IEEE. first International Conference on Neural Networks. San Diego,USA,1987.[Eds.: Caudill,M. and Butler Ch.]; Vol. III, pp. 301-308.
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Sequence in context: A110041 A064327 A134277 this_sequence A001908 A006129 A022515
Adjacent sequences: A085337 A085338 A085339 this_sequence A085341 A085342 A085343
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KEYWORD
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sign
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 08 2003
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