%I
%S 1,1,1,1,2,1,1,2,2,1,1,2,3,2,1,1,2,3,3,2,1,1,2,3,5,3,2,1,1,2,3,5,5,3,
%T 2,1,1,2,3,5,8,5,3,2,1,1,2,3,5,8,8,5,3,2,1,1,2,3,5,8,13,8,5,3,2,1,1,2,
%U 3,5,8,13,13,8,5,3,2,1,1,2,3,5,8,13,21,13,8,5,3,2,1,1,2,3,5,8
%N Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.
%C A204026 represents the matrix M given by f(i,j)=min(F(i+1),F(j+1)) for i>=1 and j>=1. See A204027 for characteristic polynomials of principal submatrices of M, with interlacing zeros. See A204016 for a guide to other choices of M.
%e Northwest corner:
%e 1 1 1 1 1 1
%e 1 2 2 2 2 2
%e 1 2 3 3 3 3
%e 1 2 3 5 5 5
%e 1 2 3 5 8 8
%e 1 2 3 5 8 13
%t f[i_, j_] := Min[Fibonacci[i + 1], Fibonacci[j + 1]]
%t m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t TableForm[m[6]] (* 6x6 principal submatrix *)
%t Flatten[Table[f[i, n + 1  i],
%t {n, 1, 15}, {i, 1, n}]] (* A204026 *)
%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[%] (* A204027 *)
%t TableForm[Table[c[n], {n, 1, 10}]]
%Y Cf. A204026, A204016, A202453.
%K nonn,tabl
%O 1,5
%A _Clark Kimberling_, Jan 11 2012
