A038379 is all wrong

Max A. maxale at gmail.com
Wed Nov 8 11:27:40 CET 2006


A038379 is defined as the "number of positive semi-definite real {0,1}
n X n matrices".
But the sequence and comments have nothing to do with the description.

In particular, all given values do not match the definition.
It lists 1, 3, 27, 729, 52649 while the correct values (that match the
definition) are 2, 7, 59, 1468, 102751 (I will be grateful if somebody
check these values).
For the simplest case n=1, it is clear that there two positive
semi-definite real {0,1}-matrices:
(0) and (1).

There is also a comment:
%C A038379 For n <= 4 a(n) = the upper bound 3^C(n,2).
Why the upper bound is 3^C(n,2) ? We have only two options for each
element of the matrix.
There would be an upper bound of this type if:
1) The main diagonal of a matrix is fixed, and the matrix is
symmetric. Then there are C(n,2) distinct non-diagonal elements whose
values should be assigned.
2) There are three (not two!) possible values for each non-diagonal
element of the matrix.

It seems that the definition of A038379 does not match the rest. Can
anybody find a definition of A038379 that is consistent with its
current content? If so, I will submit the real "number of positive
semi-definite real {0,1} n X n matrices" as a separate sequence.

Regards,
Max






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