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Search: id:A141525
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| A141525 |
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A low average ratio switched sequence: a(n)=If[Mod[n, 3] == 0, a(n - 2) + a(n - 3), If(Mod[n, 4) == 0, a(n - 1) + a(n - 4), a(n - 1), a(n - 2)]]. |
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+0
1
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| 0, 1, 1, 1, 1, 1, 2, 2, 3, 4, 4, 4, 8, 8, 8, 16, 24, 24, 40, 40, 64, 80, 80, 80, 160, 160, 160, 320, 480, 480, 800, 800, 1280, 1600, 1600, 1600, 3200, 3200, 3200, 6400, 9600
(list; table; graph; listen)
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OFFSET
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1,7
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COMMENT
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While appearing to be an "even" output or maybe a "regular" sequence the average ratio limit( using <> as expectation value):
Limit[<a(n+1)/a(n)>,n->Infinity]=1.324717957244746;
real root of x^3-x-1 ( Padovan/ minimal Pisot root).
I got this by accident I meant to type in:
a[n] = If[Mod[n, 3] == 0, a[n - 2] + a[n - 3], If[Mod[n, 4] == 0, a[n - 1] + a[n - 4], a[n - 1] + a[n - 2]]];
which gives a different result!
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REFERENCES
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.
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FORMULA
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a(n)=If[Mod[n, 3] == 0, a(n - 2) + a(n - 3), If(Mod[n, 4) == 0, a(n - 1) + a(n - 4), a(n - 1), a(n - 2)]].
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MATHEMATICA
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Clear[a] a[0] = 0; a[1] = 1; a[2] = 1; a[3] = 1; a[n_] := a[n] = If[Mod[n, 3] == 0, a[n - 2] + a[n - 3], If[Mod[n, 4] == 0, a[n - 1] + a[n - 4], a[n - 1], a[n - 2]]]; Table[a[n], {n, 0, 40}]
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CROSSREFS
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Sequence in context: A070172 A130128 A049980 this_sequence A071475 A112778 A080594
Adjacent sequences: A141522 A141523 A141524 this_sequence A141526 A141527 A141528
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KEYWORD
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nonn,uned,tabl
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 11 2008
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