A204169 - OEIS

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A204169

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (i+j-1), as in A002024.

1, -1, -1, -4, 1, 0, 6, 9, -1, 0, 0, -20, -16, 1, 0, 0, 0, 50, 25, -1, 0, 0, 0, 0, -105, -36, 1, 0, 0, 0, 0, 0, 196, 49, -1, 0, 0, 0, 0, 0, 0, -336, -64, 1, 0, 0, 0, 0, 0, 0, 0, 540, 81, -1, 0, 0, 0, 0, 0, 0, 0, 0, -825, -100, 1

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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..65.

EXAMPLE

Top of the array:

2....-1

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

0.....6.....9....-1

0.....0....-20...-16...1

MATHEMATICA

f[i_, j_] := i + j - 1;