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A204027 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of M (as in A204026), given by min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers). 3
1, -1, 1, -3, 1, 1, -5, 6, -1, 2, -12, 21, -11, 1, 6, -40, 86, -70, 19, -1, 30, -212, 508, -510, 214, -32, 1, 240, -1756, 4482, -5056, 2646, -614, 53, -1, 3120, -23308, 61748, -74480, 44002, -12764, 1703, -87, 1, 65520, -495708, 1343084 (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 and A204016 for guides to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

Top of the array:

1....-1

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

1....-5....6....-1

2....-12...21...-11....1

MATHEMATICA

f[i_, j_] := Min[Fibonacci[i + 1], Fibonacci[j + 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, 15}, {i, 1, n}]]  (* A204026 *)

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[%]                 (* A204027 *)

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

CROSSREFS

Cf. A204026, A202605, A204016.

Sequence in context: A121522 A294582 A294589 * A080842 A216948 A183944

Adjacent sequences:  A204024 A204025 A204026 * A204028 A204029 A204030

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 11 2012

STATUS

approved

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Last modified February 29 02:07 EST 2020. Contains 332353 sequences. (Running on oeis4.)