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A204133 Symmetric matrix based on f(i,j)=(2^(i-1) if i=j and 1 otherwise), by antidiagonals.

%I A204133 #5 Mar 30 2012 18:58:07
%S A204133 1,1,1,1,2,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,
%T A204133 1,1,1,1,1,1,16,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,32,1,1,1,1,1,1,
%U A204133 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,64,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A204133 Symmetric matrix based on f(i,j)=(2^(i-1) if i=j and 1 otherwise), by antidiagonals.
%C A204133 A204133 represents the matrix M given by f(i,j)=(2^(i-1) if i=j and 1 otherwise) for i>=1 and j>=1.  See A204134 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204133 Northwest corner:
%e A204133 1 1 1 1 1
%e A204133 1 2 1 1 1
%e A204133 1 1 4 1 1
%e A204133 1 1 1 6 1
%e A204133 1 1 1 1 8
%t A204133 f[i_, j_] := 1; f[i_, i_] := 2^(i - 1);
%t A204133 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204133 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204133 Flatten[Table[f[i, n + 1 - i],
%t A204133   {n, 1, 15}, {i, 1, n}]]  (* A204133 *)
%t A204133 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204133 c[n_] := CoefficientList[p[n], x]
%t A204133 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204133 Table[c[n], {n, 1, 12}]
%t A204133 Flatten[%]                 (* A204134 *)
%t A204133 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204133 Cf. A204134, A204016, A202453.
%K A204133 nonn,tabl
%O A204133 1,5
%A A204133 _Clark Kimberling_, Jan 11 2012