A017898, a Fibonacci-like sequence

[Allan Wechsler]

In the sequence oeis.org/A017898, the recurrence relation is A(n) = A(n-1) + A(n-4). The corresponding characteristic equation is x^4 - x^3 - 1 = 0, whose dominant root is in the vicinity of 1.38207; let's call that number omega. It probably already has a name, "the strontium ratio" or something like that.

So, as expected, there is some initial value K such that for n big enough to overcome some transient flutter, A(n) is the closest integer to K*omega^n. I haven't actually calculated a decent value for K. 

Is it worth including a comment to this effect, or do we usually not bother with linear recurrences?

-- Allan

[Neil Sloane]

Allan,  That information would certainly enhance the sequence, so I say go ahead and add it.  

Best regards

Neil 

Neil J. A. Sloane, Chairman, OEIS Foundation.

Also Visiting Scientist, Math. Dept., Rutgers University, 

Email: njas...@gmail.com

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[Allan Wechsler]

I need to go look at A45 to see how the archetypical description of the analogous facts is phrased. If anybody who is more ready wants grab this one from me, feel free.

-- Allan

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[Hugo Pfoertner]

The constant is the second smallest Pisot number,

https://oeis.org/A086106

More material is given in https://oeis.org/A003269