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A141525 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)]]. 0
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; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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!

REFERENCES

.

LINKS

Table of n, a(n) for n=1..41.

FORMULA

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)]].

MATHEMATICA

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}]

CROSSREFS

Sequence in context: A208914 A049980 A209698 * A209764 A071475 A112778

Adjacent sequences:  A141522 A141523 A141524 * A141526 A141527 A141528

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Aug 11 2008

STATUS

approved

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)