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A204005 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max{2i+j-2,2j+i-2} (A204004). 3
1, -1, -5, -5, 1, 9, 31, 12, -1, -13, -73, -105, -22, 1, 17, 131, 322, 265, 35, -1, -21, -205, -711, -1036, -560, -51, 1, 25, 295, 1320, 2775, 2730, 1050, 70, -1, -29, -401, -2197, -6050, -8745, -6258, -1806, -92, 1, 33, 523, 3390, 11557 (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

Table of n, a(n) for n=1..48.

EXAMPLE

Top of the array:

1....-1

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

9.....31...12....-1

-13...-73..-105...-22...1

MATHEMATICA

f[i_, j_] := Max[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}]]  (* A204004 *)

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[%]   (* A204005 *)

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

CROSSREFS

Cf. A204004, A202605.

Sequence in context: A254347 A011094 A319569 * A075298 A060058 A092766

Adjacent sequences:  A204002 A204003 A204004 * A204006 A204007 A204008

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 09 2012

STATUS

approved

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)