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A204127 Symmetric matrix based on f(i,j)=(F(i+1) if i=j and 1 otherwise), where F=A000045 (Fibonacci numbers), by antidiagonals.

%I A204127 #6 Mar 30 2012 18:58:07
%S A204127 1,1,1,1,2,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,5,1,1,1,1,1,1,1,1,1,
%T A204127 1,1,1,1,1,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,13,1,1,1,1,1,1,1,
%U A204127 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,21,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A204127 Symmetric matrix based on f(i,j)=(F(i+1) if i=j and 1 otherwise), where F=A000045 (Fibonacci numbers), by antidiagonals.
%C A204127 A204127 represents the matrix M given by f(i,j)=(F(i+1) if i=j and 1 otherwise) for i>=1 and j>=1.  See A204128 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.
%e A204127 Northwest corner:
%e A204127 1 1 1 1 1 1
%e A204127 1 2 1 1 1 1
%e A204127 1 1 3 1 1 1
%e A204127 1 1 1 5 1 1
%e A204127 1 1 1 1 8 1
%e A204127 1 1 1 1 1 13
%t A204127 f[i_, j_] := 1; f[i_, i_] := Fibonacci[i + 1];
%t A204127 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204127 TableForm[m[8]] (* 8x8 principal submatrix *)
%t A204127 Flatten[Table[f[i, n + 1 - i],
%t A204127   {n, 1, 15}, {i, 1, n}]]  (* A204127 *)
%t A204127 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204127 c[n_] := CoefficientList[p[n], x]
%t A204127 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204127 Table[c[n], {n, 1, 12}]
%t A204127 Flatten[%]                 (* A204128 *)
%t A204127 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204127 Cf. A204128, A204016, A202453.
%K A204127 nonn,tabl
%O A204127 1,5
%A A204127 _Clark Kimberling_, Jan 11 2012