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A204007 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min{2i+j-2,2j+i-2} (A204006). 3
1, -1, 0, -5, 1, -1, -1, 12, -1, -2, 7, 5, -22, 1, -3, 19, -28, -15, 35, -1, -4, 35, -99, 84, 35, -51, 1, -5, 55, -220, 375, -210, -70, 70, -1, -6, 79, -403, 990, -1155, 462, 126, -92, 1, -7, 107, -660, 2093, -3575, 3069, -924, -210, 117, -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 for a guide to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

Top of the array:

1....-1

0....-5....1

-1....-1....12....-1

-2.....7....5.....-22...1

MATHEMATICA

f[i_, j_] := Min[2 i + j - 2, 2 j + i - 2];

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}]]   (* A204006 *)

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[%]                (* A204007 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204006, A202605.

Sequence in context: A010130 A206773 A229526 * A242404 A145295 A091051

Adjacent sequences:  A204004 A204005 A204006 * A204008 A204009 A204010

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 09 2012

STATUS

approved

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Last modified April 25 16:59 EDT 2019. Contains 322461 sequences. (Running on oeis4.)