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A097565
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a(0) = 0, a(1) = 1, a(n) = (a(n-1) mod F(n))*a(n-1) + a(n-2) for n > 2 where F(n) is the n-th Fibonacci number.
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1
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0, 1, 0, 1, 1, 2, 5, 27, 167, 5204, 177103, 14527650, 959002003, 94955725947, 4084055217724, 179793385305803, 120106065439494128, 183522247784932333387, 256013655766046044568993, 173321428475860957105541648
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OFFSET
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0,6
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COMMENTS
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The fractional portion of a(n)/a(n-1) exponentially approaches 0 as n increases.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..100
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MATHEMATICA
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RecurrenceTable[{a[0]==0, a[1]==1, a[n]==Mod[a[n-1], Fibonacci[n]]a[n-1]+ a[n-2]}, a, {n, 20}] (* Harvey P. Dale, Jul 06 2016 *)
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PROG
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(Magma)
a:= func< n | n le 2 select n-1 else (Self(n-1) mod Fibonacci(n-1))*Self(n-1) + Self(n-2) >;
[a(n): n in [1..21]]; // G. C. Greubel, Apr 20 2021
(Sage)
@CachedFunction
def a(n): return n if (n<2) else (a(n-1)%fibonacci(n))*a(n-1) + a(n-2)
[a(n) for n in (0..20)] # G. C. Greubel, Apr 20 2021
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CROSSREFS
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Sequence in context: A100105 A087130 A265266 * A079716 A322151 A355765
Adjacent sequences: A097562 A097563 A097564 * A097566 A097567 A097568
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KEYWORD
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nonn
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AUTHOR
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Gerald McGarvey, Aug 27 2004
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STATUS
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approved
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