cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A084552 Number of n X n symmetric positive definite matrices with 2's on the main diagonal and -1's and 0's elsewhere.

Original entry on oeis.org

1, 2, 7, 38, 286, 2686, 28512, 312572, 3337588, 40963216
Offset: 1

Views

Author

N. J. A. Sloane, Jul 13 2003

Keywords

Comments

Of course the total number of symmetric matrices of this type (not necessarily positive definite) is 2^C(n,2).
This gives the number of different values of M + M' where M runs through the matrices counted in A127502.

Examples

			The singular matrix
2 -1 -1
-1 2 -1
-1 -1 2
is the only 3 X 3 matrix of this type which is not positive definite.

Links

Crossrefs

Cf. A084553, A085659, A080858, A083029.

Extensions

a(6)-a(10) from Max Alekseyev, Jan 16 2006

A127503 Number of n X n matrices A with 1's on the main diagonal and -1's and 0's elsewhere such that A + A' has only 0's and -1's off the main diagonal and is positive semi-definite.

Original entry on oeis.org

1, 3, 27, 281, 3945, 70635, 1437555, 30357425, 628337745
Offset: 1

Views

Author

Max Alekseyev, Jan 16 2007

Keywords

Comments

For number of different values of A + A' see A084553.

Crossrefs

Cf. A085657, A085658, A080858, A083029, A038379, A127502.
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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