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 A204167 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of floor[(i+j)/2], as in A204164. 3
 1, -1, -2, -3, 1, 1, 6, 6, -1, 0, -4, -16, -10, 1, 0, 0, 15, 32, 15, -1, 0, 0, 0, -36, -60, -21, 1, 0, 0, 0, 0, 84, 100, 28, -1, 0, 0, 0, 0, 0, -160, -160, -36, 1, 0, 0, 0, 0, 0, 0, 300, 240, 45, -1, 0, 0, 0, 0, 0, 0, 0, -500, -350 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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: 1....-1 -2....-3.....1 1.....6.....6....-1 0....-4....-16...-10...1 MATHEMATICA f[i_, j_] := Ceiling[(i + j)/2]; 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}]]  (* A204166 *) 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[%]                 (* A204167 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A204166, A202605, A204016. Sequence in context: A182933 A068348 A308290 * A217897 A135900 A173272 Adjacent sequences:  A204164 A204165 A204166 * A204168 A204169 A204170 KEYWORD tabl,sign AUTHOR Clark Kimberling, Jan 12 2012 STATUS approved

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Last modified February 27 09:44 EST 2020. Contains 332301 sequences. (Running on oeis4.)