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A203996 Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals.

%I A203996 #12 Jul 08 2024 11:11:27
%S A203996 2,3,3,4,6,4,5,8,8,5,6,10,12,10,6,7,12,15,15,12,7,8,14,18,20,18,14,8,
%T A203996 9,16,21,24,24,21,16,9,10,18,24,28,30,28,24,18,10,11,20,27,32,35,35,
%U A203996 32,27,20,11,12,22,30,36,40,42,40,36,30,22,12,13,24,33,40,45,48
%N A203996 Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals.
%C A203996 A203996 represents the matrix M given by f(i,j)=min{i(j+1),j(i+1)} for i>=1 and j>=1.  See A203997 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A203996 Northwest corner:
%e A203996 2...3....4....5....6....7
%e A203996 3...6....8....10...12...14
%e A203996 4...8....12...15...18...21
%e A203996 5...10...15...20...24...28
%t A203996 f[i_, j_] := Min[i (j + 1), j (i + 1)];
%t A203996 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A203996 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A203996 Flatten[Table[f[i, n + 1 - i],
%t A203996 {n, 1, 12}, {i, 1, n}]]   (* A203996 *)
%t A203996 p[n_] := CharacteristicPolynomial[m[n], x];
%t A203996 c[n_] := CoefficientList[p[n], x]
%t A203996 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A203996 Table[c[n], {n, 1, 12}]
%t A203996 Flatten[%]      (* A203997 *)
%t A203996 TableForm[Table[c[n], {n, 1, 10}]]
%Y A203996 Cf. A203995, A202453.
%K A203996 nonn,tabl
%O A203996 1,1
%A A203996 _Clark Kimberling_, Jan 09 2012