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A110033 A characteristic triangle for the Fibonacci numbers.

%I A110033 #5 Mar 30 2012 18:59:08
%S A110033 1,-1,1,1,-3,1,0,3,-8,1,0,0,9,-21,1,0,0,0,24,-55,1,0,0,0,0,64,-144,1,
%T A110033 0,0,0,0,0,168,-377,1,0,0,0,0,0,0,441,-987,1,0,0,0,0,0,0,0,1155,-2584,
%U A110033 1,0,0,0,0,0,0,0,0,3025,-6765,1,0,0,0,0,0,0,0,0,0,7920,-17711,1
%N A110033 A characteristic triangle for the Fibonacci numbers.
%F A110033 Form the n X n Hankel matrices F(i+j-1), 1<=i, j<=n for the Fibonacci numbers and take the characteristic polynomials of these matrices. Triangle rows give coefficients of these characteristic polynomials. (Construction described by Michael Somos in A064831). Diagonal is (-1)^n*F(2n+2). Subdiagonal is A064831. Row sums are A110034. The unsigned matrix has row sums A110035.
%e A110033 Rows begin
%e A110033 1;
%e A110033 -1,1;
%e A110033 1,-3,1;
%e A110033 0,3,-8,1;
%e A110033 0,0,9,-21,1;
%e A110033 0,0,0,24,-55,1;
%e A110033 0,0,0,0,64,-144,1;
%e A110033 0,0,0,0,0,168,-377,1;
%K A110033 sign,tabl
%O A110033 0,5
%A A110033 _Paul Barry_, Jul 08 2005