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A204001 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min{i(j+1-1),j(i+1)-1} (A204000). 3
1, -1, 1, -6, 1, 1, -9, 17, -1, 1, -12, 39, -36, 1, 1, -15, 69, -119, 65, -1, 1, -18, 107, -272, 294, -106, 1, 1, -21, 153, -515, 846, -630, 161, -1, 1, -24, 207, -868, 1925, -2232, 1218, -232, 1, 1, -27, 269, -1351, 3783, -6017, 5214 (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..51.

EXAMPLE

Top of the array:

1...-1

1...-6....1

1...-9....17...-1

1...-12...39...-36...1

MATHEMATICA

f[i_, j_] := Min[i (j + 1) - 1, j (i + 1) - 1];

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}]]  (* A204000 *)

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[%]               (* A204001 *)

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

CROSSREFS

Cf. A204000, A202605.

Sequence in context: A144470 A174377 A176151 * A144395 A046621 A046617

Adjacent sequences:  A203998 A203999 A204000 * A204002 A204003 A204004

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 09 2012

STATUS

approved

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Last modified September 18 09:05 EDT 2021. Contains 347518 sequences. (Running on oeis4.)