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A204015 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min{1+(j mod i), 1+( i mod j)} (A204014). 3
1, -1, 0, -2, 1, -1, 3, 3, -1, 0, 2, -6, -4, 1, 0, -8, 8, 20, 5, -1, -16, 14, 58, -4, -31, -6, 1, 48, 16, -169, -121, 69, 63, 7, -1, 208, -320, -576, 540, 432, -128, -97, -8, 1, 400, -2048, 1876, 2340, -1828, -928, 309, 153, 9, -1, -4800, 6880 (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 for a guide to related sequences.

REFERENCES

(For references regarding interlacing roots, see A202605.)

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

Top of the array:

1...-1

0...-2...1

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

0....2..-6...-4....1

0...-8...8....20...5...1

MATHEMATICA

f[i_, j_] := Min[1 + Mod[i, j], 1 + Mod[j, i]];

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[6]] (* 6x6 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

{n, 1, 12}, {i, 1, n}]]  (* A204014 *)

p[n_] := CharacteristicPolynomial[m[n], x];

c[n_] := CoefficientList[p[n], x]

TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

Table[c[n], {n, 1, 12}]

Flatten[%]   (* A204015 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204014, A202605.

Sequence in context: A275865 A136458 A048805 * A216210 A186332 A129571

Adjacent sequences:  A204012 A204013 A204014 * A204016 A204017 A204018

KEYWORD

tabl,sign

AUTHOR

Clark Kimberling, Jan 10 2012

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)