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Search: id:A109521
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| A109521 |
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a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,3*(n-1)]. |
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| -1, -3, -34, -675, -19024, -693000, -30932712, -1634065377, -99689107456, -6896573452773, -533453984900000, -45619590554955648, -4273735683350974464, -435258791936039363799, -47881430324748383440000, -5658033217549016808984375, -714765666389657378401288192
(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)=-675 because if M is the 2 X 2 matrix [0,-1;3,9], then M^4 is the 2 X 2 matrix [ -234,-675;2025,5841].
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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, 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);
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MATHEMATICA
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M[n_] = If[n > 1, MatrixPower[{{0, -1}, {n - 1, 3*(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: A143638 A126753 A047794 this_sequence A069718 A077144 A101633
Adjacent sequences: A109518 A109519 A109520 this_sequence A109522 A109523 A109524
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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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