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Expansion of x*(1-2*x-x^2)/( (1-x)*(1+x)*(1-3*x+x^2)).
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%I #20 Sep 08 2022 08:45:18

%S 0,1,1,2,3,7,16,41,105,274,715,1871,4896,12817,33553,87842,229971,

%T 602071,1576240,4126649,10803705,28284466,74049691,193864607,

%U 507544128,1328767777,3478759201,9107509826,23843770275,62423800999,163427632720,427859097161

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

%C The real roots of the denominator function are x = +-1, A104457 and A132338.

%H Vincenzo Librandi, <a href="/A107387/b107387.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-3,1).

%F a(n) = 1 + A001654(n-2).

%t LinearRecurrence[{3,0,-3,1},{0,1,1,2},50] (* _Vincenzo Librandi_, Aug 22 2012 *)

%t CoefficientList[Series[x (1-2x-x^2)/((1-x)(1+x)(1-3x+x^2)),{x,0,40}],x] (* _Harvey P. Dale_, May 31 2020 *)

%o (Magma) I:=[ 0,1,1,2]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-3) +Self(n-4): n in [1..40]] // _Vincenzo Librandi_, Aug 22 2012

%K nonn,easy

%O 0,4

%A _Roger L. Bagula_, May 24 2005, corrected Sep 04 2008

%E Replaced with a regular sequence by _R. J. Mathar_, Aug 31 2011