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