A204144 - OEIS

A204144

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j)=max(ceiling(i/j),ceiling(j/i)) (as in A204143).

1, -1, -3, -2, 1, 8, 14, 3, -1, -12, -42, -35, -4, 1, 19, 95, 145, 73, 5, -1, -20, -140, -338, -336, -125, -6, 1, 16, 184, 665, 1037, 735, 205, 7, -1, -16, -212, -981, -2140, -2381, -1320, -303, -8, 1, 12, 200, 1209, 3581, 5727, 5021

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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..50.

EXAMPLE

Top of the array:

1...-1

-3...-2....1

8....14...3....-1

-12..-42..-35...-4....1

MATHEMATICA

f[i_, j_] := Max[Ceiling[i/j], Ceiling[j/i]];