A203992 - OEIS

A203992

Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (A143182 in square format).

1, -1, -3, -2, 1, 8, 14, 3, -1, -20, -56, -40, -4, 1, 48, 184, 224, 90, 5, -1, -112, -544, -936, -672, -175, -6, 1, 256, 1504, 3344, 3480, 1680, 308, 7, -1, -576, -3968, -10816, -14784, -10560, -3696, -504, -8, 1, 1280, 10112, 32640, 55328

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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 for a guide to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

Top of the array:

1... -1

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

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

-20.. -56.. -40.. -4... 1

MATHEMATICA

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