A204161 - OEIS

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A204161

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (3i-2 if i=j and = 0 otherwise), as in A204160.

1, -1, 3, -5, 1, 18, -36, 12, -1, 162, -360, 153, -22, 1, 1944, -4644, 2295, -435, 35, -1, 29160, -73548, 40419, -9135, 990, -51, 1, 524880, -1382184, 823284, -210924, 27720, -1953, 70, -1, 11022480

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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..36.

EXAMPLE

Top of the array:

1.....-1

3.....-5.....1

18....-36....12....-1

162...-360...153...-22...1

MATHEMATICA

f[i_, j_] := 1; f[i_, i_] := 2 i - 1;