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A111641 Expansion of -(1+x+3*x^2+x^3)/((x^2+4*x+1)*(x^2-2*x-1)). 7

%I

%S 1,-5,25,-107,433,-1697,6529,-24839,93841,-352973,1323961,-4957139,

%T 18539041,-69282185,258790465,-966364367,3607837153,-13467809237,

%U 50270219929,-187629535739,700287673681,-2613617125553,9754412512321,-36404592257879,135865306871281

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

%C In reference to the program code, the sequence of Pell numbers A000126 is given by 1kbaseseq[C*J]. A001353 is 1ibaseiseq[C*J].

%H Colin Barker, <a href="/A111641/b111641.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-6,-8,2,1).

%F a(n) = -6*a(n-1) - 8*a(n-2) + 2*a(n-3) + a(n-4) for n>3. - _Colin Barker_, Apr 29 2019

%t CoefficientList[Series[-(1+x+3x^2+x^3)/((x^2+4x+1)(x^2-2x-1)),{x,0,30}],x] (* or *) LinearRecurrence[{-6,-8,2,1},{1,-5,25,-107},30] (* _Harvey P. Dale_, Oct 12 2017 *)

%o Floretion Algebra Multiplication Program, FAMP Code: 1lestesseq[C*J] with C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki' and J = + j' + k' + 1.5'ii' + .5'jj' + .5'kk' + .5e

%o (PARI) Vec((1 + x + 3*x^2 + x^3) / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^25)) \\ _Colin Barker_, Apr 29 2019

%Y Cf. A111639, A111640, A111642, A111643, A111644, A000126.

%K easy,sign

%O 0,2

%A _Creighton Dement_, Aug 10 2005

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Last modified May 15 03:54 EDT 2021. Contains 343909 sequences. (Running on oeis4.)