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A204174 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (f(i,j)), where f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise) as in A204173. 2
1, -1, 0, -1, 1, -4, 6, 3, -1, 0, 4, -6, -3, 1, 36, -60, -31, 33, 6, -1, 0, -36, 60, 31, -33, -6, 1, -576, 1008, 516, -736, -131, 105, 10, -1, 0, 576, -1008, -516, 736, 131, -105, -10, 1, 14400, -25920, -13116, 21628, 3621, -4581, -406, 255 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

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..52.

EXAMPLE

Top of the array:

1...-1

0...-1....1

4....6....3...-1

0....4...-6...-3...1

MATHEMATICA

f[i_, j_] := If[Mod[Max[i, j], 2] == 1,

(1 + Max[i, j])/2, 0]

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}]]  (* A204173 *)

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[%]                 (* A204174 *)

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

CROSSREFS

Cf. A202605, A204016, A204173.

Sequence in context: A212084 A182368 A185442 * A086467 A197731 A138508

Adjacent sequences:  A204171 A204172 A204173 * A204175 A204176 A204177

KEYWORD

tabf,sign

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified January 22 19:50 EST 2020. Contains 331153 sequences. (Running on oeis4.)