A109518 a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;n-1,3(n-1)].

1, 3, 38, 783, 22480, 828000, 37231704, 1977187485, 121098539008, 8403438270285, 651608685100000, 55835951178466800, 5239593453691293696, 534383614812622168191, 58857325474654519917440

Offset: 1

Author

Roger L. Bagula, Jun 16 2005

Keywords

• nonn

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)=783 because if M is the 2 X 2 matrix [0,1;3,9], then M^4 is the 2 X 2 matrix [252,783,2349,7299].
		

Crossrefs

Cf. A000045, A000166.

Programs

Maple

with(linalg): a:=proc(n) local A,k: A[1]:=matrix(2,2,[0,1,n-1,3*(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..18);

Mathematica

M[n_] = If[n > 1, MatrixPower[{{0, 1}, {n - 1, 3*(n - 1)}}, n], {{0, 1}, {1, 1}}] a = Table[M[n][[1, 2]], {n, 1, 50}]