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A204159 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(3i-2j, 3j-2i), as in A204158. 3
1, -1, -14, -3, 1, 115, 79, 6, -1, -800, -895, -255, -10, 1, 5125, 7875, 3850, 625, 15, -1, -31250, -60875, -42075, -12180, -1295, -21, 1, 184375, 434375, 387750, 162375, 31710, 2394, 28, -1, -1062500, -2934375 (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..37.

EXAMPLE

Top of the array:

1.....-1

-14....-3......1

115....79.....6.....-1

-800...-895...-255...-10....1

MATHEMATICA

f[i_, j_] := Max[3 i - 2 j, 3 j - 2 i];

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[8]] (* 8x8 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]   (* A204158 *)

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[%]                 (* A204159 *)

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

CROSSREFS

Cf. A204158, A202605, A204016.

Sequence in context: A242061 A040189 A088576 * A040190 A317314 A163647

Adjacent sequences:  A204156 A204157 A204158 * A204160 A204161 A204162

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified April 20 02:06 EDT 2019. Contains 322291 sequences. (Running on oeis4.)