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 A204168 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (i+j), as in A003057. 2
 2, -1, -1, -6, 1, 0, 6, 12, -1, 0, 0, -20, -20, 1, 0, 0, 0, 50, 30, -1, 0, 0, 0, 0, -105, -42, 1, 0, 0, 0, 0, 0, 196, 56, -1, 0, 0, 0, 0, 0, 0, -336, -72, 1, 0, 0, 0, 0, 0, 0, 0, 540, 90, -1, 0, 0, 0, 0, 0, 0, 0, 0, -825, -110, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix.  The zeros of p(n) are real, and they interlace the zeros of p(n+1).  See A202605 and A204016 for guides to related sequences. REFERENCES (For references regarding interlacing roots, see A202605.) LINKS EXAMPLE Top of the array: 2....-1 -1....-6.....1 0.....6.....12....-1 0.....0....-20....-20...1 MATHEMATICA f[i_, j_] := i + j; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[8]] (* 8x8 principal submatrix *) Flatten[Table[f[i, n + 1 - i],   {n, 1, 15}, {i, 1, n}]]  (* A003057 *) p[n_] := CharacteristicPolynomial[m[n], x]; c[n_] := CoefficientList[p[n], x] TableForm[Flatten[Table[p[n], {n, 1, 10}]]] Table[c[n], {n, 1, 12}] Flatten[%]                 (* A204168 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A003057, A202605, A204016. Sequence in context: A025264 A321716 A245567 * A216914 A216917 A216919 Adjacent sequences:  A204165 A204166 A204167 * A204169 A204170 A204171 KEYWORD tabl,sign AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified March 28 07:45 EDT 2020. Contains 333079 sequences. (Running on oeis4.)