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A202875 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A202874; by antidiagonals.

%I A202875 #12 Oct 02 2017 09:58:33
%S A202875 1,-1,1,-6,1,1,-12,20,-1,1,-19,69,-59,1,1,-27,159,-303,162,-1,1,-36,
%T A202875 302,-943,1149,-434,1,1,-46,511,-2284,4599,-3991,1147,-1,1,-57,800,
%U A202875 -4743,13733,-19785,13090,-3016,1,1,-69,1184,-8867,34141,-70945
%N A202875 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A202874; by antidiagonals.
%C A202875 Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix. The zeros of p(n) are positive, and they interlace the zeros of p(n+1).
%H A202875 S.-G. Hwang, <a href="http://matrix.skku.ac.kr/Series-E/Monthly-E.pdf">Cauchy's interlace theorem for eigenvalues of Hermitian matrices</a>, American Mathematical Monthly 111 (2004) 157-159.
%H A202875 A. Mercer and P. Mercer, <a href="http://dx.doi.org/10.1155/S016117120000257X">Cauchy's interlace theorem and lower bounds for the spectral radius</a>, International Journal of Mathematics and Mathematical Sciences 23, no. 8 (2000) 563-566.
%e A202875 Top of the array:
%e A202875 1...-1
%e A202875 1...-6....1
%e A202875 1...-12...20...-1
%e A202875 1...-19...69...-59...1
%t A202875 f[k_] := Fibonacci[k + 1]
%t A202875 U[n_] := NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[f[k], {k, 1, n}]];
%t A202875 L[n_] := Transpose[U[n]];
%t A202875 F[n_] := CharacteristicPolynomial[L[n].U[n], x];
%t A202875 c[n_] := CoefficientList[F[n], x]
%t A202875 TableForm[Flatten[Table[F[n], {n, 1, 10}]]]
%t A202875 Table[c[n], {n, 1, 12}]
%t A202875 Flatten[%]
%t A202875 TableForm[Table[c[n], {n, 1, 10}]]
%Y A202875 Cf. A202874, A202605.
%K A202875 tabl,sign
%O A202875 1,4
%A A202875 _Clark Kimberling_, Dec 26 2011