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A204123 Symmetric matrix based on f(i,j)=max([i/j],[j/i]), where [ ]=floor, by antidiagonals.

%I A204123 #11 Jan 27 2018 09:47:44
%S A204123 1,2,2,3,1,3,4,1,1,4,5,2,1,2,5,6,2,1,1,2,6,7,3,1,1,1,3,7,8,3,2,1,1,2,
%T A204123 3,8,9,4,2,1,1,1,2,4,9,10,4,2,1,1,1,1,2,4,10,11,5,3,2,1,1,1,2,3,5,11,
%U A204123 12,5,3,2,1,1,1,1,2,3,5,12,13,6,3,2,1,1,1,1,1,2,3,6,13,14,6,4,2
%N A204123 Symmetric matrix based on f(i,j)=max([i/j],[j/i]), where [ ]=floor, by antidiagonals.
%C A204123 This sequence represents the matrix M given by f(i,j)=max([i/j],[j/i]) for i>=1 and j>=1.  See A204124 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%H A204123 G. C. Greubel, <a href="/A204123/b204123.txt">Table of n, a(n) for the first 100 aintidiagonals</a>
%e A204123 Northwest corner:
%e A204123 1 2 3 4 5 6
%e A204123 2 1 1 2 2 3
%e A204123 3 1 1 1 1 2
%e A204123 4 2 1 1 1 1
%e A204123 5 2 1 1 1 1
%e A204123 6 3 2 1 1 1
%t A204123 f[i_, j_] := Max[Floor[i/j], Floor[j/i]];
%t A204123 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204123 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204123 Flatten[Table[f[i, n + 1 - i],
%t A204123   {n, 1, 15}, {i, 1, n}]]  (* A204123 *)
%t A204123 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204123 c[n_] := CoefficientList[p[n], x]
%t A204123 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204123 Table[c[n], {n, 1, 12}]
%t A204123 Flatten[%]                 (* A204124 *)
%t A204123 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204123 Cf. A204124, A204016, A202453.
%K A204123 nonn,tabl
%O A204123 1,2
%A A204123 _Clark Kimberling_, Jan 11 2012