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Expansion of 1/(1 - x - x^2 + x^18 - x^20).
4

%I #21 Mar 12 2017 09:34:59

%S 1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,4180,6763,

%T 10942,17703,28642,46340,74974,121301,196254,317521,513720,831152,

%U 1344728,2175647,3519998,5695035,9214046,14907484,24118947,39022252,63134437,102145749

%N Expansion of 1/(1 - x - x^2 + x^18 - x^20).

%C Limiting ratio is 1.61791..., the real root of -1 + x^2 - x^18 - x^19 + x^20. Signature in Mathematica is:

%C -CoefficientList[1 - x - x^2 + x^18 - x^20, x]

%C {-1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1}.

%C The sequence agrees with the Fibonacci numbers (A000045) for the first 18 terms.

%H G. C. Greubel, <a href="/A185357/b185357.txt">Table of n, a(n) for n = 0..1000</a>

%H David Terr and Eric W. Weisstein, <a href="http://mathworld.wolfram.com/PisotNumber.html">MathWorld: Pisot Number</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1).

%t CoefficientList[Series[1/(1 - x - x^2 + x^18 - x^20), {x, 0, 50}], x]

%o (PARI) Vec(1/(1-x-x^2+x^18-x^20) + O(x^50)) \\ _G. C. Greubel_, Nov 16 2016

%Y Cf. A117791, A107293, A204631.

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Jan 21 2012