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A204157 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(3i-j, 3j-i), as in A204156. 3
1, -1, -13, -4, 1, 88, 78, 9, -1, -496, -704, -260, -16, 1, 2560, 4960, 3080, 650, 25, -1, -12544, -30720, -26784, -9856, -1365, -36, 1, 59392, 175616, 197120, 104160, 25872, 2548, 49, -1, -274432, -950272, -1304576, -901120, -327360, -59136, -4368, -64, 1, 1245184, 4939776, 8017920, 6849024, 3294720 (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..49.

EXAMPLE

Top of the array:

1....-1

-13...-4.....1

88....78....9.....-1

-496..-704..-260...-16...1

MATHEMATICA

f[i_, j_] := -1 + Max[3 i - j, 3 j - 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}]]    (* A204156 *)

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[%]                   (* A204157 *)

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

CROSSREFS

Cf. A204156, A202605, A204016.

Sequence in context: A298137 A155847 A204594 * A010219 A217426 A056139

Adjacent sequences:  A204154 A204155 A204156 * A204158 A204159 A204160

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified March 21 20:30 EDT 2019. Contains 321382 sequences. (Running on oeis4.)