A204023 - OEIS

A204023

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(2i-1, 2j-1) (A204022).

1, -1, -6, -4, 1, 20, 36, 9, -1, -56, -160, -120, -16, 1, 144, 560, 700, 300, 25, -1, -352, -1728, -3024, -2240, -630, -36, 1, 832, 4928, 11088, 11760, 5880, 1176, 49, -1, -1920, -13312, -36608, -50688, -36960

(list; table; graph; refs; listen; history; text; internal format)

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..40.

EXAMPLE

Top of the array:

1....-1

-6....-4.....1

20....36....9.....-1

-56...-160..-120...-16....1

MATHEMATICA

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