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%I #16 Apr 03 2019 09:38:01
%S 0,6,18,40,76,130,206,308,440,606,810,1056,1348,1690,2086,2540,3056,
%T 3638,4290,5016,5820,6706,7678,8740,9896,11150,12506,13968,15540,
%U 17226,19030,20956,23008,25190,27506,29960,32556,35298,38190,41236,44440
%N Sum of squares of entries of Wilkinson's eigenvalue test matrix of order 2n+1.
%C 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_, May 24 2002
%F 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_, May 24 2002
%F a(n) = sum(2*(k+1)^2+4, k=0..(n-1)). - _Mike Warburton_, Sep 08 2007
%F G.f.: 2*x*(3-3*x+2*x^2)/(1-x)^4. - _Colin Barker_, Apr 04 2012
%e The matrix of order 5:
%e 2 1 0 0 0
%e 1 1 1 0 0
%e 0 1 0 1 0
%e 0 0 1 1 1
%e 0 0 0 1 2
%o (MATLAB) for i = 0:20 a(i+1) = trace( wilkinson(2*i+1)*wilkinson(2*i+1)' ); end; a
%Y Cf. A059831.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Feb 25 2001
%E More terms from _David Wasserman_, May 24 2002
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