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A204006 Symmetric matrix based on f(i,j) = min{2i+j-2,i+2j-2}, by antidiagonals.

%I A204006 #13 Feb 06 2023 14:03:33
%S A204006 1,2,2,3,4,3,4,5,5,4,5,6,7,6,5,6,7,8,8,7,6,7,8,9,10,9,8,7,8,9,10,11,
%T A204006 11,10,9,8,9,10,11,12,13,12,11,10,9,10,11,12,13,14,14,13,12,11,10,11,
%U A204006 12,13,14,15,16,15,14,13,12,11,12,13,14,15,16,17,17,16,15,14,13,12
%N A204006 Symmetric matrix based on f(i,j) = min{2i+j-2,i+2j-2}, by antidiagonals.
%C A204006 A204006 represents the matrix M given by f(i,j) = min{2i+j,i+2j} for i>=1 and j>=1.  See A204007 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A204006 Northwest corner:
%e A204006 1...2...3...4....5....6
%e A204006 2...4...5...6....7....8
%e A204006 3...5...7...8....9....10
%e A204006 4...6...8...10...11...12
%t A204006 f[i_, j_] := Min[2 i + j - 2, 2 j + i - 2];
%t A204006 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204006 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204006 Flatten[Table[f[i, n + 1 - i],
%t A204006 {n, 1, 12}, {i, 1, n}]]   (* A204006 *)
%t A204006 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204006 c[n_] := CoefficientList[p[n], x]
%t A204006 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204006 Table[c[n], {n, 1, 12}]
%t A204006 Flatten[%]                (* A204007 *)
%t A204006 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204006 Cf. A204007, A202453.
%K A204006 nonn,tabl
%O A204006 1,2
%A A204006 _Clark Kimberling_, Jan 09 2012