A109520 a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,2*(n-1)].

-1, -2, -14, -180, -3344, -80750, -2394792, -84150248, -3417051136, -157409163162, -8109659900000, -462005414448732, -28837128777928704, -1956971256267512966, -143459789419986793600, -11297467798871681250000, -951158499840260908777472

Offset: 1

Author

Roger L. Bagula, Jun 16 2005

Keywords

• sign

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).

Examples

			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].
		

Crossrefs

Cf. A000045, A000166.

Programs

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}]