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.
%I A364886 #26 Oct 18 2023 09:21:51 %S A364886 1,2,20,640,97824,47545088 %N A364886 Number of n X n (-1, 1)-matrices which have only eigenvalues with strictly negative real part (which implies that the matrix has all nonzero eigenvalues). %C A364886 As this problem is symmetric with sign we can get the same numbers for strictly positive real parts. %C A364886 All values for n > 1 are even, because a transposed matrix has the same spectrum of eigenvalues. %C A364886 Matrices with determinant 0 are not counted. %C A364886 Let M be such a matrix then the limit of ||exp(t*M)*y|| if t goes to infinity will be zero. %C A364886 n = 5 is the first case where not all entries on the main diagonal are -1. 93984 matrices with 5 times -1 on the main diagonal and 5*768 with 4 times -1 on the main diagonal have only eigenvalues with strictly negative real part. %C A364886 In the case n = 6, 43586048 matrices with 6 times -1 on the main diagonal, 6*656000 matrices with 5 times -1 on the main diagonal and 15*1536 matrices with 5 times -1 on the main diagonal have only eigenvalues with strictly negative real part. %H A364886 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a> %e A364886 For n = 2 the matrices are: %e A364886 . %e A364886 -1, 1 %e A364886 -1, -1 %e A364886 . %e A364886 -1, -1 %e A364886 1, -1. %Y A364886 Cf. A056990. %Y A364886 Cf. A083058, A085506, A087488, A098148, A086510, A207259. %Y A364886 Cf. A219736, A346210, A271570, A271588, A296605, A306002. %Y A364886 Cf. A306791, A306792, A306793, A306794, A306795, A326928. %Y A364886 Cf. A346209. %K A364886 nonn,more %O A364886 1,2 %A A364886 _Thomas Scheuerle_, Aug 12 2023