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 A203992 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (A143182 in square format). 2
 1, -1, -3, -2, 1, 8, 14, 3, -1, -20, -56, -40, -4, 1, 48, 184, 224, 90, 5, -1, -112, -544, -936, -672, -175, -6, 1, 256, 1504, 3344, 3480, 1680, 308, 7, -1, -576, -3968, -10816, -14784, -10560, -3696, -504, -8, 1, 1280, 10112, 32640, 55328 (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 for a guide to related sequences. REFERENCES (For references regarding interlacing roots, see A202605.) LINKS EXAMPLE Top of the array: 1... -1 -3... -1.... 1 8.... 14... 3... -1 -20.. -56.. -40.. -4... 1 MATHEMATICA f[i_, j_] := Max[i - j + 1, j - i + 1]; m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}] TableForm[m[6]] (* 6x6 principal submatrix *) Flatten[Table[f[i, n + 1 - i], {n, 1, 12}, {i, 1, n}]] (* A143182 in square format *) 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[%] (* A203992 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A143182, A202605. Sequence in context: A104552 A210803 A204144 * A204019 A196846 A101413 Adjacent sequences: A203989 A203990 A203991 * A203993 A203994 A203995 KEYWORD tabl,sign AUTHOR Clark Kimberling, Jan 09 2012 STATUS approved

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Last modified December 5 02:30 EST 2022. Contains 358572 sequences. (Running on oeis4.)