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A204026 Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.

%I A204026 #5 Mar 30 2012 18:58:07
%S A204026 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 A204026 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 A204026 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 A204026 Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.
%C A204026 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 A204026 Northwest corner:
%e A204026 1 1 1 1 1 1
%e A204026 1 2 2 2 2 2
%e A204026 1 2 3 3 3 3
%e A204026 1 2 3 5 5 5
%e A204026 1 2 3 5 8 8
%e A204026 1 2 3 5 8 13
%t A204026 f[i_, j_] := Min[Fibonacci[i + 1], Fibonacci[j + 1]]
%t A204026 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204026 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204026 Flatten[Table[f[i, n + 1 - i],
%t A204026   {n, 1, 15}, {i, 1, n}]]  (* A204026 *)
%t A204026 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204026 c[n_] := CoefficientList[p[n], x]
%t A204026 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204026 Table[c[n], {n, 1, 12}]
%t A204026 Flatten[%]                 (* A204027 *)
%t A204026 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204026 Cf. A204026, A204016, A202453.
%K A204026 nonn,tabl
%O A204026 1,5
%A A204026 _Clark Kimberling_, Jan 11 2012