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Search: id:A109520
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| A109520 |
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a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,2*(n-1)]. |
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1
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| -1, -2, -14, -180, -3344, -80750, -2394792, -84150248, -3417051136, -157409163162, -8109659900000, -462005414448732, -28837128777928704, -1956971256267512966, -143459789419986793600, -11297467798871681250000, -951158499840260908777472
(list; graph; listen)
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OFFSET
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1,2
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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)=-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].
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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, 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);
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000045, A000166.
Sequence in context: A084946 A047055 A046247 this_sequence A000807 A074655 A067902
Adjacent sequences: A109517 A109518 A109519 this_sequence A109521 A109522 A109523
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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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