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Expansion of (1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5).
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%I #21 Sep 08 2022 08:45:19

%S 1,1,1,1,1,4,4,7,10,16,25,37,58,88,136,208,319,490,751,1153,1768,2713,

%T 4162,6385,9796,15028,23056,35371,54265,83251,127720,195943,300607,

%U 461179,707521,1085449,1665250,2554756,3919399,6012976,9224854,14152381

%N Expansion of (1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5).

%H Peter Borwein and Kevin G. Hare, <a href="https://docserver.carma.newcastle.edu.au/id/eprint/225">Some Computations on Pisot and Salem Numbers</a>, CARMA Preprint, 2000, p.7, Table 1.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,1,1).

%F a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5).

%t LinearRecurrence[{0, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, 50]

%t CoefficientList[Series[(1+x-x^3-2x^4)/(1-x^2-x^3-x^4-x^5),{x,0,50}],x] (* _Harvey P. Dale_, Oct 24 2021 *)

%o (Maxima) makelist(ratcoef(taylor((1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5), x, 0, n), x, n), n, 0, 50); /* _Franck Maminirina Ramaharo_, Oct 31 2018 */

%o (PARI) x='x+O('x^50); Vec((1+x-x^3-2*x^4)/(1-x^2-x^3-x^4-x^5)) \\ _G. C. Greubel_, Nov 03 2018

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x-x^3-2*x^4)/(1-x^2-x^3-x^4-x^5))); // _G. C. Greubel_, Nov 03 2018

%Y Cf. A013982.

%Y Cf. A107479, A107480, A109538, A109543, A114749, A125950, A130844, A143335, A147851.

%K nonn,easy

%O 0,6

%A _Roger L. Bagula_, Jun 20 2005