Search: id:A059834
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%I A059834
%S A059834 0,6,18,40,76,130,206,308,440,606,810,1056,1348,1690,2086,2540,3056,
%T A059834 3638,4290,5016,5820,6706,7678,8740,9896,11150,12506,13968,15540,17226,
%U A059834 19030,20956,23008,25190,27506,29960,32556,35298,38190,41236,44440
%N A059834 Sum of squares of entries of Wilkinson's eigenvalue test matrix of order 
               2n+1.
%C A059834 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
%F A059834 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
%F A059834 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
%e A059834 The matrix of order 5:
%e A059834 2 1 0 0 0
%e A059834 1 1 1 0 0
%e A059834 0 1 0 1 0
%e A059834 0 0 1 1 1
%e A059834 0 0 0 1 2
%o A059834 (MATLAB) for i = 0:20 a(i+1) = trace( wilkinson(2*i+1)*wilkinson(2*i+1)' 
               ); end; a
%Y A059834 Cf. A059831.
%Y A059834 Sequence in context: A122061 A002411 A023658 this_sequence A015224 A163983 
               A023620
%Y A059834 Adjacent sequences: A059831 A059832 A059833 this_sequence A059835 A059836 
               A059837
%K A059834 nonn
%O A059834 0,2
%A A059834 N. J. A. Sloane (njas(AT)research.att.com), Feb 25 2001
%E A059834 More terms from David Wasserman (wasserma(AT)spawar.navy.mil), May 24 
               2002

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