OFFSET
1,2
COMMENTS
The (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;1,1] is the Fibonacci number A000045(n).
EXAMPLE
a(4)=-180 because if M is the 2 X 2 matrix [0,-1;3,6], then M^4 is the 2 X 2 matrix [ -99,-180,540,981].
MAPLE
with(linalg): a:=proc(n) local A, k: A[1]:=matrix(2, 2, [0, -1, n-1, 2*(n-1)]): for k from 2 to n do A[k]:=multiply(A[k-1], A[1]) od: A[n][1, 2] end: seq(a(n), n=1..19);
MATHEMATICA
M[n_] = If[n > 1, MatrixPower[{{0, -1}, {n - 1, 2*(n - 1)}}, n], {{0, 1}, {1, 1}}] a = Table[Abs[M[n][[1, 2]]], {n, 1, 50}]
CROSSREFS
KEYWORD
sign
AUTHOR
Roger L. Bagula, Jun 16 2005
STATUS
approved