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A204002 Symmetric matrix based on f(i,j)=min{2i+j,i+2j}, by antidiagonals.

%I A204002 #5 Mar 30 2012 18:58:07
%S A204002 3,4,4,5,6,5,6,7,7,6,7,8,9,8,7,8,9,10,10,9,8,9,10,11,12,11,10,9,10,11,
%T A204002 12,13,13,12,11,10,11,12,13,14,15,14,13,12,11,12,13,14,15,16,16,15,14,
%U A204002 13,12,13,14,15,16,17,18,17,16,15,14,13,14,15,16,17,18,19,19
%N A204002 Symmetric matrix based on f(i,j)=min{2i+j,i+2j}, by antidiagonals.
%C A204002 A204002 represents the matrix M given by f(i,j)=min{2i+j,i+2j}for i>=1 and j>=1.  See A204003 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A204002 Northwest corner:
%e A204002 3...4...5....6....7....8
%e A204002 4...6...7....8....9....10
%e A204002 5...7...9....10...11...12
%e A204002 6...8...10...12...13...14
%t A204002 f[i_, j_] := Min[2 i + j, 2 j + i];
%t A204002 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204002 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204002 Flatten[Table[f[i, n + 1 - i],
%t A204002 {n, 1, 12}, {i, 1, n}]]    (* A204002 *)
%t A204002 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204002 c[n_] := CoefficientList[p[n], x]
%t A204002 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204002 Table[c[n], {n, 1, 12}]
%t A204002 Flatten[%]                 (* A204003 *)
%t A204002 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204002 Cf. A204003, A202453.
%K A204002 nonn,tabl
%O A204002 1,1
%A A204002 _Clark Kimberling_, Jan 09 2012