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Search: id:A059834
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| A059834 |
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Sum of squares of entries of Wilkinson's eigenvalue test matrix of order 2n+1. |
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+0
2
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| 0, 6, 18, 40, 76, 130, 206, 308, 440, 606, 810, 1056, 1348, 1690, 2086, 2540, 3056, 3638, 4290, 5016, 5820, 6706, 7678, 8740, 9896, 11150, 12506, 13968, 15540, 17226, 19030, 20956, 23008, 25190, 27506, 29960, 32556, 35298, 38190, 41236, 44440
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The m X m Wilkinson matrix is a symmetric tridiagonal matrix. If m = 2k + 1, its main diagonal is k, k - 1, ..., 1, 0, 1, ... k - 1, k. If m = 2k, its main diagonal is k - 1/2, k - 3/2, ..., 3/2, 1/2, 1/2, 3/2, ..., k - 3/2, k - 1/2. In both cases, it has all 1's on the diagonals next to the main diagonal and 0's elsewhere. - David Wasserman (wasserma(AT)spawar.navy.mil), May 24 2002
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FORMULA
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a(n) = (2n^3 + 3n^2 + 13n)/3. For the matrix of order 2n, the formula is (4n^3 + 23n - 12)/6 (which is not integer-valued). - David Wasserman (wasserma(AT)spawar.navy.mil), May 24 2002
An alternative formula for this sequence is Sum(2*(k+1)^2+4, k=0..(n-1)) This can be confirmed in Maple/Mathematica. - Mike Warburton (mikewarb(AT)gmail.com), Sep 08 2007
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EXAMPLE
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The matrix of order 5:
2 1 0 0 0
1 1 1 0 0
0 1 0 1 0
0 0 1 1 1
0 0 0 1 2
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PROGRAM
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(MATLAB) for i = 0:20 a(i+1) = trace( wilkinson(2*i+1)*wilkinson(2*i+1)' ); end; a
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CROSSREFS
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Cf. A059831.
Sequence in context: A122061 A002411 A023658 this_sequence A015224 A163983 A023620
Adjacent sequences: A059831 A059832 A059833 this_sequence A059835 A059836 A059837
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Feb 25 2001
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), May 24 2002
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