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A202877 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A202875; by antidiagonals.

%I A202877 #13 Oct 02 2017 09:58:39
%S A202877 1,-1,1,-6,1,1,-11,27,-1,1,-17,84,-97,1,1,-23,177,-497,311,-1,1,-29,
%T A202877 306,-1405,2546,-925,1,1,-35,471,-3034,9375,-11628,2628,-1,1,-41,672,
%U A202877 -5599,24817,-55080,48875,-7247,1,1,-47,909,-9316,54164
%N A202877 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A202875; by antidiagonals.
%C A202877 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 A202877 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 A202877 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 A202877 Top of the array:
%e A202877 1...-1
%e A202877 1...-6....1
%e A202877 1...-11...27...-1
%e A202877 1...-17...84...-97...1
%t A202877 f[k_] := -1 + Fibonacci[k + 2]
%t A202877 U[n_] :=NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[f[k], {k, 1, n}]];
%t A202877 L[n_] := Transpose[U[n]];
%t A202877 F[n_] := CharacteristicPolynomial[L[n].U[n], x];
%t A202877 c[n_] := CoefficientList[F[n], x]
%t A202877 TableForm[Flatten[Table[F[n], {n, 1, 10}]]]
%t A202877 Table[c[n], {n, 1, 12}]
%t A202877 Flatten[%]
%t A202877 TableForm[Table[c[n], {n, 1, 10}]]
%Y A202877 Cf. A202876, A202605.
%K A202877 tabl,sign
%O A202877 1,4
%A A202877 _Clark Kimberling_, Dec 26 2011