A059834 Sum of squares of entries of Wilkinson's eigenvalue test matrix of order 2n+1.

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

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..40.

Formula

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

a(n) = sum(2*(k+1)^2+4, k=0..(n-1)). - Mike Warburton, Sep 08 2007

G.f.: 2*x*(3-3*x+2*x^2)/(1-x)^4. - Colin Barker, Apr 04 2012

Example

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

Prog

(MATLAB) for i = 0:20 a(i+1) = trace( wilkinson(2*i+1)*wilkinson(2*i+1)' ); end; a

Crossrefs

Cf. A059831.

Sequence in context: A299256 A002411 A023658 * A299263 A015224 A163983

Adjacent sequences: A059831 A059832 A059833 * A059835 A059836 A059837

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 25 2001

Extensions

More terms from David Wasserman, May 24 2002

Status

approved