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 A203002 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A203001; by antidiagonals. 2
 1, -1, 1, -3, 1, 1, -14, 21, -1, 1, -29, 162, -120, 1, 1, -48, 540, -1736, 844, -1, 1, -71, 1267, -8091, 17022, -5664, 1, 1, -98, 2475, -24908, 105503, -158690, 39045, -1, 1, -129, 4312, -60994, 408508, -1250056, 1416673 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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). LINKS S.-G. Hwang, Cauchy's interlace theorem for eigenvalues of Hermitian matrices, American Mathematical Monthly 111 (2004) 157-159. A. Mercer and P. Mercer, Cauchy's interlace theorem and lower bounds for the spectral radius, International Journal of Mathematics and Mathematical Sciences 23, no. 8 (2000) 563-566. EXAMPLE Top of the array: 1...-1 1...-3....1 1...-14...21....-1 1...-29...162...-120...1 MATHEMATICA f[k_] := Fibonacci[k]^2; U[n_] := NestList[Most[Prepend[#, 0]] &, #, Length[#] - 1] &[Table[f[k], {k, 1, n}]]; L[n_] := Transpose[U[n]]; F[n_] := CharacteristicPolynomial[L[n].U[n], x]; c[n_] := CoefficientList[F[n], x] TableForm[Flatten[Table[F[n], {n, 1, 10}]]] Table[c[n], {n, 1, 12}] Flatten[%] TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A203001, A202605. Sequence in context: A174690 A156869 A153090 * A073483 A006956 A072285 Adjacent sequences:  A202999 A203000 A203001 * A203003 A203004 A203005 KEYWORD tabl,sign AUTHOR Clark Kimberling, Dec 27 2011 STATUS approved

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Last modified April 19 04:19 EDT 2019. Contains 322237 sequences. (Running on oeis4.)