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A204159 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(3i-2j, 3j-2i), as in A204158.

%I A204159 #6 Jul 12 2012 00:39:58
%S A204159 1,-1,-14,-3,1,115,79,6,-1,-800,-895,-255,-10,1,5125,7875,3850,625,15,
%T A204159 -1,-31250,-60875,-42075,-12180,-1295,-21,1,184375,434375,387750,
%U A204159 162375,31710,2394,28,-1,-1062500,-2934375
%N A204159 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max(3i-2j, 3j-2i), as in A204158.
%C A204159 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 A204159 (For references regarding interlacing roots, see A202605.)
%e A204159 Top of the array:
%e A204159  1.....-1
%e A204159 -14....-3......1
%e A204159  115....79.....6.....-1
%e A204159 -800...-895...-255...-10....1
%t A204159 f[i_, j_] := Max[3 i - 2 j, 3 j - 2 i];
%t A204159 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204159 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204159 Flatten[Table[f[i, n + 1 - i],
%t A204159   {n, 1, 15}, {i, 1, n}]]   (* A204158 *)
%t A204159 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204159 c[n_] := CoefficientList[p[n], x]
%t A204159 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204159 Table[c[n], {n, 1, 12}]
%t A204159 Flatten[%]                 (* A204159 *)
%t A204159 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204159 Cf. A204158, A202605, A204016.
%K A204159 tabl,sign
%O A204159 1,3
%A A204159 _Clark Kimberling_, Jan 12 2012