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Search: id:A109517
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| A109517 |
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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, 2, 18, 252, 4880, 120750, 3639384, 129365880, 5298720768, 245738908890, 12728860100000, 728372947109940, 45631105330876416, 3106354479972026374, 228329428483544787840, 18022862954171193750000
(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)=252 because if M is the 2 X 2 matrix [0,1;3,6], then M^4 is the 2 X 2 matrix [117,252;756;1629].
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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[M[n][[1, 2]], {n, 1, 50}]
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CROSSREFS
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Cf. A000045, A000166.
Sequence in context: A117514 A138437 A121429 this_sequence A099880 A032037 A138275
Adjacent sequences: A109514 A109515 A109516 this_sequence A109518 A109519 A109520
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 16 2005
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