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Search: id:A109516
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| A109516 |
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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, 1, 6, 45, 464, 6000, 93528, 1707111, 35721216, 843160671, 22165100000, 642268811184, 20339749638144, 698946255836933, 25903663544572800, 1029945249481640625, 43733528272753917952, 1975222567881226040760
(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)=45 because if M is the 2 X 2 matrix [0,1;3,3], then M^4 is the 2 X 2 matrix [36,45;135;171].
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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..20);
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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[M[n][[1, 2]], {n, 1, 50}]
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CROSSREFS
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Cf. A000045, A000166.
Sequence in context: A019577 A097814 A084064 this_sequence A078865 A160492 A086721
Adjacent sequences: A109513 A109514 A109515 this_sequence A109517 A109518 A109519
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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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