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A204029 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j)=min(3i-2,3j-2) (A204028).

%I A204029 #6 Jul 12 2012 00:39:58
%S A204029 1,-1,3,-5,1,9,-21,12,-1,27,-81,75,-22,1,81,-297,378,-195,35,-1,243,
%T A204029 -1053,1701,-1260,420,-51,1,729,-3645,7128,-6885,3402,-798,70,-1,2187,
%U A204029 -12393,28431,-33858,22275,-7938,1386,-92,1,6561
%N A204029 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of f(i,j)=min(3i-2,3j-2) (A204028).
%C A204029 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.
%D A204029 (For references regarding interlacing roots, see A202605.)
%e A204029 Top of the array:
%e A204029 1....-1
%e A204029 3....-5....1
%e A204029 9....-21...12...-1
%e A204029 27...-81...75...-22....-11
%t A204029 f[i_, j_] := Min[3 i - 2, 3 j - 2];
%t A204029 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204029 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204029 Flatten[Table[f[i, n + 1 - i],
%t A204029   {n, 1, 15}, {i, 1, n}]]  (* A204028 *)
%t A204029 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204029 c[n_] := CoefficientList[p[n], x]
%t A204029 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204029 Table[c[n], {n, 1, 12}]
%t A204029 Flatten[%]                 (* A204029 *)
%t A204029 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204029 Cf. A204028, A202605, A204016.
%K A204029 tabl,sign
%O A204029 1,3
%A A204029 _Clark Kimberling_, Jan 11 2012