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A204014 Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.

%I A204014 #5 Mar 30 2012 18:58:07
%S A204014 1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,2,2,2,2,1,1,1,3,1,3,1,1,1,2,1,2,2,1,
%T A204014 2,1,1,1,2,3,1,3,2,1,1,1,2,3,4,2,2,4,3,2,1,1,1,1,1,3,1,3,1,1,1,1,1,2,
%U A204014 2,2,4,2,2,4,2,2,2,1,1,1,3,3,5,3,1,3,5,3,3,1,1,1,2,1,4,1,4,2,2
%N A204014 Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.
%C A204014 A204014 represents the matrix M given by f(i,j)=min{1+(j mod i), 1+( i mod j)} for i>=1 and j>=1.  See A204015 for characteristic polynomials of principal submatrices of M, with interlacing zeros.
%e A204014 Northwest corner:
%e A204014 1 1 1 1 1 1
%e A204014 1 1 2 1 2 1
%e A204014 1 2 1 2 3 1
%e A204014 1 1 2 1 2 3
%e A204014 1 2 3 2 1 2
%t A204014 f[i_, j_] := Min[1 + Mod[i, j], 1 + Mod[j, i]];
%t A204014 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204014 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204014 Flatten[Table[f[i, n + 1 - i],
%t A204014 {n, 1, 12}, {i, 1, n}]]  (* A204014 *)
%t A204014 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204014 c[n_] := CoefficientList[p[n], x]
%t A204014 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204014 Table[c[n], {n, 1, 12}]
%t A204014 Flatten[%]               (* A204015 *)
%t A204014 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204014 Cf. A204015, A202453.
%K A204014 nonn,tabl
%O A204014 1,8
%A A204014 _Clark Kimberling_, Jan 10 2012