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.

A084553 Number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and -1's and 0's elsewhere.

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%I A084553 #8 Jun 05 2024 23:50:24
%S A084553 1,2,8,45,338,3178,34346,396659,4694705
%N A084553 Number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and -1's and 0's elsewhere.
%C A084553 Of course the total number of symmetric matrices of this type (not necessarily positive definite) is 2^C(n,2).
%C A084553 This gives the number of different values of A + A' where A runs through the matrices counted in A127503.
%H A084553 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%e A084553 The 5 X 5 matrix
%e A084553 2 -1 -1 -1 -1
%e A084553 -1 2 -1 -1 -1
%e A084553 -1 -1 2 -1 -1
%e A084553 -1 -1 -1 2 -1
%e A084553 -1 -1 -1 -1 2
%e A084553 with eigenvalues -2, 3, 3, 3, 3 is an example of one which is not positive semi-definite.
%Y A084553 Cf. A084552, A085658, A080858, A083029.
%K A084553 nonn,more
%O A084553 1,2
%A A084553 _N. J. A. Sloane_, Jul 13 2003
%E A084553 a(6)-a(9) from _Max Alekseyev_, Jan 16 2006