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Search: id:A109519
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| A109519 |
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a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,n-1]. |
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1
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| -1, -1, -2, -9, -80, -1000, -15336, -276115, -5705728, -133155495, -3464900000, -99490865760, -3125217447936, -106614813012877, -3925516139359360, -155164259295703125, -6553564019985219584, -294562012662334323872, -14038370700094085018112
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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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).
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EXAMPLE
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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].
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MAPLE
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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);
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MATHEMATICA
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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}]
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PROGRAM
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sage: [ -lucas_number1(n+1, n, n) for n in xrange(0, 19)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 16 2008
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CROSSREFS
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Cf. A000045, A000166.
Sequence in context: A111196 A056918 A122720 this_sequence A135868 A147302 A112670
Adjacent sequences: A109516 A109517 A109518 this_sequence A109520 A109521 A109522
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KEYWORD
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sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 16 2005
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