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A204143 Symmetric matrix based on f(i,j)=max(ceiling(i/j),ceiling(j/i)), by antidiagonals.

%I A204143 #6 Mar 30 2012 18:58:07
%S A204143 1,2,2,3,1,3,4,2,2,4,5,2,1,2,5,6,3,2,2,3,6,7,3,2,1,2,3,7,8,4,2,2,2,2,
%T A204143 4,8,9,4,3,2,1,2,3,4,9,10,5,3,2,2,2,2,3,5,10,11,5,3,2,2,1,2,2,3,5,11,
%U A204143 12,6,4,3,2,2,2,2,3,4,6,12,13,6,4,3,2,2,1,2,2,3,4,6,13,14,7,4,3
%N A204143 Symmetric matrix based on f(i,j)=max(ceiling(i/j),ceiling(j/i)), by antidiagonals.
%C A204143 A204143 represents the matrix M given by f(i,j)=max(ceiling(i/j),ceiling(j/i)) for i>=1 and j>=1.  See A204144 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204143 Northwest corner:
%e A204143 1 2 3 4 5 6
%e A204143 2 1 2 2 3 3
%e A204143 3 2 1 2 2 2
%e A204143 4 2 2 1 2 2
%e A204143 5 3 2 2 1 2
%e A204143 6 3 2 2 2 1
%t A204143 f[i_, j_] := Max[Ceiling[i/j], Ceiling[j/i]];
%t A204143 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204143 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204143 Flatten[Table[f[i, n + 1 - i],
%t A204143   {n, 1, 15}, {i, 1, n}]]  (* A204143 *)
%t A204143 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204143 c[n_] := CoefficientList[p[n], x]
%t A204143 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204143 Table[c[n], {n, 1, 12}]
%t A204143 Flatten[%]                 (* A204144 *)
%t A204143 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204143 Cf. A204144, A204016, A202453.
%K A204143 nonn,tabl
%O A204143 1,2
%A A204143 _Clark Kimberling_, Jan 11 2012