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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 June 6 01:16 EDT 2020. Contains 334858 sequences. (Running on oeis4.)