A204113 - OEIS

A204113

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the matrix at A204112, given by f(i,j) = gcd(F(i+1), F(j+1)), where F=A000045 (Fibonacci numbers).

1, -1, 1, -3, 1, 2, -8, 6, -1, 8, -36, 35, -11, 1, 48, -232, 274, -116, 19, -1, 576, -2880, 3620, -1728, 358, -32, 1, 10368, -52992, 70632, -37192, 8906, -1016, 53, -1, 331776, -1716480, 2354112, -1294352, 332812, -42924, 2805

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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..42.

EXAMPLE

Top of the array:

1, -1;

1, -3, 1;

2, -8, 6, -1;

8, -36, 35, -11, 1;

MATHEMATICA

u[n_] := Fibonacci[n + 1]