A204184 - OEIS

A204184

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (f(i,j)), where f(i,1)=f(1,j)=1, f(i,i)=(-1)^(i-1); f(i,j)=0 otherwise; as in A204181.

1, -1, -2, 0, 1, -1, 3, 1, -1, 2, -2, -5, 0, 1, 1, -5, -2, 6, 1, -1, -2, 4, 9, -4, -8, 0, 1, -1, 7, 3, -15, -3, 9, 1, -1, 2, -6, -13, 12, 21, -6, -11, 0, 1, 1, -9, -4, 28, 6, -30, -4, 12, 1, -1, -2, 8, 17, -24, -40, 24, 38, -8, -14, 0, 1, -1, 11, 5

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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..68.

EXAMPLE

Top of the array:

1..-1

2...0...1

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

2..-2..-5...0..1

MATHEMATICA

f[i_, j_] := 0; f[1, j_] := 1; f[i_, 1] := 1;