A110033 A characteristic triangle for the Fibonacci numbers.

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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3025, -6765, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7920, -17711, 1

Offset

0,5

Links

Table of n, a(n) for n=0..77.

Formula

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.

Example

Rows begin
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;
0,0,0,0,0,168,-377,1;

Crossrefs

Sequence in context: A122016 A067882 A215771 * A213666 A166407 A285123

Adjacent sequences: A110030 A110031 A110032 * A110034 A110035 A110036

Keyword

sign,tabl

Author

Paul Barry, Jul 08 2005

Status

approved