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%I A203998 #7 Mar 30 2012 18:58:07
%S A203998 1,3,3,5,5,5,7,8,8,7,9,11,11,11,9,11,14,15,15,14,11,13,17,19,19,19,17,
%T A203998 13,15,20,23,24,24,23,20,15,17,23,27,29,29,29,27,23,17,19,26,31,34,35,
%U A203998 35,34,31,26,19,21,29,35,39,41,41,41,39,35,29,21,23,32,39,44
%N A203998 Symmetric matrix based on f(i,j)=max{i(j+1)-1,j(i+1)-1}, by antidiagonals.
%C A203998 A203998 represents the matrix M given by f(i,j)=max{i(j+1)-1,j(i+1)-1}for i>=1 and j>=1.  See A203999 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A203998 Northwest corner:
%e A203998 1...3....5....7....9
%e A203998 3...5....8....11...14
%e A203998 5...8....11...15...19
%e A203998 7...11...15...19...24
%t A203998 f[i_, j_] := Max[i (j + 1) - 1, j (i + 1) - 1];
%t A203998 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A203998 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A203998 Flatten[Table[f[i, n + 1 - i],
%t A203998 {n, 1, 12}, {i, 1, n}]]    (* A203998 *)
%t A203998 p[n_] := CharacteristicPolynomial[m[n], x];
%t A203998 c[n_] := CoefficientList[p[n], x]
%t A203998 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A203998 Table[c[n], {n, 1, 12}]
%t A203998 Flatten[%]   (* A203999 *)
%t A203998 TableForm[Table[c[n], {n, 1, 10}]]
%Y A203998 Cf. A203999, A202453.
%K A203998 nonn,tabl
%O A203998 1,2
%A A203998 _Clark Kimberling_, Jan 09 2012

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