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 A204169 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (i+j-1), as in A002024. 2
 1, -1, -1, -4, 1, 0, 6, 9, -1, 0, 0, -20, -16, 1, 0, 0, 0, 50, 25, -1, 0, 0, 0, 0, -105, -36, 1, 0, 0, 0, 0, 0, 196, 49, -1, 0, 0, 0, 0, 0, 0, -336, -64, 1, 0, 0, 0, 0, 0, 0, 0, 540, 81, -1, 0, 0, 0, 0, 0, 0, 0, 0, -825, -100, 1 (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 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....-4.....1 0.....6.....9....-1 0.....0....-20...-16...1 MATHEMATICA f[i_, j_] := i + j - 1; 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}]]  (* A002024 *) 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[%]                (* A204169 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A002024, A202605, A204016. Sequence in context: A303126 A292404 A060196 * A255331 A296794 A119305 Adjacent sequences:  A204166 A204167 A204168 * A204170 A204171 A204172 KEYWORD tabl,sign AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)