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A204005 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max{2i+j-2,2j+i-2} (A204004).

%I A204005 #7 Jul 12 2012 00:39:54
%S A204005 1,-1,-5,-5,1,9,31,12,-1,-13,-73,-105,-22,1,17,131,322,265,35,-1,-21,
%T A204005 -205,-711,-1036,-560,-51,1,25,295,1320,2775,2730,1050,70,-1,-29,-401,
%U A204005 -2197,-6050,-8745,-6258,-1806,-92,1,33,523,3390,11557
%N A204005 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of max{2i+j-2,2j+i-2} (A204004).
%C A204005 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 A204005 (For references regarding interlacing roots, see A202605.)
%e A204005 Top of the array:
%e A204005 1....-1
%e A204005 -5....-5....1
%e A204005 9.....31...12....-1
%e A204005 -13...-73..-105...-22...1
%t A204005 f[i_, j_] := Max[2 i + j - 2, 2 j + i - 2];
%t A204005 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204005 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204005 Flatten[Table[f[i, n + 1 - i],
%t A204005 {n, 1, 12}, {i, 1, n}]]  (* A204004 *)
%t A204005 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204005 c[n_] := CoefficientList[p[n], x]
%t A204005 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204005 Table[c[n], {n, 1, 12}]
%t A204005 Flatten[%]   (* A204005 *)
%t A204005 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204005 Cf. A204004, A202605.
%K A204005 tabl,sign
%O A204005 1,3
%A A204005 _Clark Kimberling_, Jan 09 2012