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Expansion of 1/(1 - x - x^2 - x^6 + x^8).
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%I #29 Sep 08 2022 08:46:04

%S 1,1,2,3,5,8,14,23,38,63,104,172,285,472,781,1293,2140,3542,5863,9705,

%T 16064,26590,44013,72852,120588,199603,330392,546880,905221,1498363,

%U 2480159,4105273,6795236,11247786,18617851,30817120,51009909,84433939,139758925

%N Expansion of 1/(1 - x - x^2 - x^6 + x^8).

%C Limiting ratio is 1.65525..., the largest real root of 1 - x^2 - x^6 - x^7 + x^8.

%H G. C. Greubel, <a href="/A225391/b225391.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,0,1,0,-1).

%F a(n) = a(n-1) + a(n-2) + a(n-6) - a(n-8). - _Franck Maminirina Ramaharo_, Nov 02 2018

%t CoefficientList[Series[1/(1 - x - x^2 - x^6 + x^8), {x, 0, 50}], x]

%t LinearRecurrence[{1,1,0,0,0,1,0,-1}, {1,1,2,3,5,8,14,23}, 100] (* _G. C. Greubel_, Nov 16 2016 *)

%o (PARI) Vec(1/(1-x-x^2-x^6+x^8) + O(x^50)) \\ _G. C. Greubel_, Nov 16 2016

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^2-x^6+x^8))); // _G. C. Greubel_, Nov 03 2018

%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A204631, A225393, A225394, A225482, A225499.

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, May 06 2013