cp's OEIS Frontend

A204027 Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of M (as in A204026), given by min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers).

%I A204027 #6 Jul 12 2012 00:39:58
%S A204027 1,-1,1,-3,1,1,-5,6,-1,2,-12,21,-11,1,6,-40,86,-70,19,-1,30,-212,508,
%T A204027 -510,214,-32,1,240,-1756,4482,-5056,2646,-614,53,-1,3120,-23308,
%U A204027 61748,-74480,44002,-12764,1703,-87,1,65520,-495708,1343084
%N A204027 Array:  row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of M (as in A204026), given by min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers).
%C A204027 Let p(n)=p(n,x) be the characteristic polynomial of the n-th principal submatrix.  The zeros of p(n) are real, and they interlace the zeros of p(n+1).  See A202605 and A204016 for guides to related sequences.
%D A204027 (For references regarding interlacing roots, see A202605.)
%e A204027 Top of the array:
%e A204027 1....-1
%e A204027 1....-3....1
%e A204027 1....-5....6....-1
%e A204027 2....-12...21...-11....1
%t A204027 f[i_, j_] := Min[Fibonacci[i + 1], Fibonacci[j + 1]]
%t A204027 m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
%t A204027 TableForm[m[6]] (* 6x6 principal submatrix *)
%t A204027 Flatten[Table[f[i, n + 1 - i],
%t A204027   {n, 1, 15}, {i, 1, n}]]  (* A204026 *)
%t A204027 p[n_] := CharacteristicPolynomial[m[n], x];
%t A204027 c[n_] := CoefficientList[p[n], x]
%t A204027 TableForm[Flatten[Table[p[n], {n, 1, 10}]]]
%t A204027 Table[c[n], {n, 1, 12}]
%t A204027 Flatten[%]                 (* A204027 *)
%t A204027 TableForm[Table[c[n], {n, 1, 10}]]
%Y A204027 Cf. A204026, A202605, A204016.
%K A204027 tabl,sign
%O A204027 1,4
%A A204027 _Clark Kimberling_, Jan 11 2012