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