Is there a way to generate the Fibonacci sequence with the Accumulate function?
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2 Answers
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fibSequences[n_?EvenQ] := Nest[Accumulate[Join[{1, 0}, #]] &, {}, n/2]
fibSequences[n_?OddQ] := Most@Nest[Accumulate[Join[{1, 0}, #]] &, {}, (n + 1)/2]
fibSequences[10]
{1, 1, 2, 3, 5, 8, 13, 21, 34, 55}
fibSequences[9]
{1, 1, 2, 3, 5, 8, 13, 21, 34}
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$\begingroup$ Nice! Wish I'd seen that myself. $\endgroup$ Commented Aug 13, 2015 at 1:42
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$\begingroup$ Probably a good time for
Nothing:Nest[Accumulate[{1, 0} ~Join~ #] &, {If[OddQ[n], 1, Nothing]}, Quotient[n, 2]]$\endgroup$ Commented Aug 13, 2015 at 17:12 -
$\begingroup$ @J. M., It is the first time for me to know the built-in
Nothing.Thanks :) I searched the DOC, then I known that it was introduced in V10.2 $\endgroup$– xyzCommented Aug 14, 2015 at 1:12
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Well... I did use Accumulate!
First /@ NestList[{Last @ #, Last @* Accumulate @ #} &, {0, 1}, 10]
{0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55}
Accumulate[Fibonacci[Range[-1, 18]]] === Fibonacci[Range[20]]. You probably would be more interested inLinearRecurrence[]. $\endgroup$