A204163 - OEIS

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A204163

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (floor[(i+1)/2] if i=j and = 0 otherwise), as in A204162.

1, -1, 0, -2, 1, 0, -2, 4, -1, 0, -2, 7, -6, 1, 0, -4, 17, -21, 9, -1, 0, -8, 40, -64, 43, -12, 1, 0, -24, 132, -244, 206, -85, 16, -1, 0, -72, 432, -904, 913, -492, 142, -20, 1, 0, -288, 1836, -4180, 4749, -3025, 1118, -234, 25, -1, 0

(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..55.

EXAMPLE

Top of the array:

1....-1

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

0....-2....4....-1

0....-4....17...-21...9...1

MATHEMATICA

f[i_, j_] := 1; f[i_, i_] := Floor[(i + 1)/2];