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 A203991 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of {(i+j)*min(i,j)} (A203990). 3
 2, -1, 7, -10, 1, 38, -71, 28, -1, 281, -610, 357, -60, 1, 2634, -6329, 4620, -1253, 110, -1, 29919, -77530, 65613, -23348, 3514, -182, 1, 399342, -1098271, 1036044, -442349, 90800, -8442, 280, -1, 6125265 (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 for a guide to related sequences. REFERENCES (For references regarding interlacing roots, see A202605.) LINKS Table of n, a(n) for n=1..36. EXAMPLE Top of the array: 2.... -1 7.... -10... 1 38... -71... 28... -1 281.. -610.. 357.. -60... 1 MATHEMATICA f[i_, j_] := (i + j) Min[i, j]; 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}]] (* A203990 *) 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[%] (* A203991 *) TableForm[Table[c[n], {n, 1, 10}]] CROSSREFS Cf. A203990, A202605. Sequence in context: A032210 A032135 A032039 * A075118 A100245 A275320 Adjacent sequences: A203988 A203989 A203990 * A203992 A203993 A203994 KEYWORD tabl,sign AUTHOR Clark Kimberling, Jan 09 2012 STATUS approved

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Last modified May 19 13:25 EDT 2024. Contains 372694 sequences. (Running on oeis4.)