A110033 - OEIS

%I #5 Mar 30 2012 18:59:08

%S 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 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 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 A characteristic triangle for the Fibonacci numbers.

%F 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 Rows begin

%e 1;

%e -1,1;

%e 1,-3,1;

%e 0,3,-8,1;

%e 0,0,9,-21,1;

%e 0,0,0,24,-55,1;

%e 0,0,0,0,64,-144,1;

%e 0,0,0,0,0,168,-377,1;

%K sign,tabl

%O 0,5

%A _Paul Barry_, Jul 08 2005