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A109519 a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,n-1]. 0
-1, -1, -2, -9, -80, -1000, -15336, -276115, -5705728, -133155495, -3464900000, -99490865760, -3125217447936, -106614813012877, -3925516139359360, -155164259295703125, -6553564019985219584, -294562012662334323872, -14038370700094085018112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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).

LINKS

Table of n, a(n) for n=1..19.

EXAMPLE

a(4)=-9 because if M is the 2 X 2 matrix [0,-1;3,3], then M^4 is the 2 X 2 matrix [ -18,-9,27,9].

MAPLE

with(linalg): a:=proc(n) local A, k: A[1]:=matrix(2, 2, [0, -1, n-1, 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..21);

MATHEMATICA

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

PROG

(Sage) [ -lucas_number1(n+1, n, n) for n in xrange(0, 19)] # Zerinvary Lajos, Jul 16 2008

CROSSREFS

Cf. A000045, A000166.

Sequence in context: A215629 A221460 A122720 * A193208 A279055 A135868

Adjacent sequences:  A109516 A109517 A109518 * A109520 A109521 A109522

KEYWORD

sign

AUTHOR

Roger L. Bagula, Jun 16 2005

STATUS

approved

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Last modified December 11 11:31 EST 2017. Contains 295876 sequences.