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A204024 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min(i(i+1)/2, j(j+1)/2) (A106255). 2
1, -1, 2, -4, 1, 6, -16, 10, -1, 24, -76, 70, -20, 1, 120, -428, 496, -224, 35, -1, 720, -2808, 3808, -2260, 588, -56, 1, 5040, -21096, 32152, -23008, 8140, -1344, 84, -1, 40320, -178848, 298688, -245560, 107328, -24772, 2772 (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 and A204016 for guides to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..42.

EXAMPLE

Top of the array:

1....-1

2....-4....1

6....-16...10...-1

24...-76...70...-20....1

MATHEMATICA

f[i_, j_] := Min[i (i + 1)/2, j (j + 1)/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, 15}, {i, 1, n}]]     (* A106255 *)

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[%]                    (* A204024 *)

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

CROSSREFS

Cf. A106255, A202605, A204016.

Sequence in context: A110877 A204115 A204130 * A021009 A137478 A089087

Adjacent sequences:  A204021 A204022 A204023 * A204025 A204026 A204027

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

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Last modified February 19 09:33 EST 2020. Contains 332041 sequences. (Running on oeis4.)