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%I #6 Jul 12 2012 00:39:54
%S 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,
%T 1,48,16,-169,-121,69,63,7,-1,208,-320,-576,540,432,-128,-97,-8,1,400,
%U -2048,1876,2340,-1828,-928,309,153,9,-1,-4800,6880
%N 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).
%C 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.
%D (For references regarding interlacing roots, see A202605.)
%e Top of the array:
%e 1...-1
%e 0...-2...1
%e -1....3...3...-1
%e 0....2..-6...-4....1
%e 0...-8...8....20...5...1
%t f[i_, j_] := Min[1 + Mod[i, j], 1 + Mod[j, i]];
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[6]] (* 6x6 principal submatrix *)
%t Flatten[Table[f[i, n + 1 - i],
%t {n, 1, 12}, {i, 1, n}]] (* A204014 *)
%t p[n_] := CharacteristicPolynomial[m[n], x];
%t c[n_] := CoefficientList[p[n], x]
%t TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t Table[c[n], {n, 1, 12}]
%t Flatten[%] (* A204015 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A204014, A202605.
%K tabl,sign
%O 1,4
%A _Clark Kimberling_, Jan 10 2012
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