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A111644 Expansion of -(1+x^2)/((x^2+4*x+1)*(x^2-2*x-1)). 4

%I

%S 1,-6,29,-124,501,-1962,7545,-28696,108393,-407662,1528981,-5724500,

%T 21408221,-80003026,298832369,-1115878064,4166011601,-15551383382,

%U 58047283725,-216656490156,808623915973,-3017948390522,11263433318761,-42036421446600,156883789264441

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

%F a(0)=1, a(1)=-6, a(2)=29, a(3)=-124, a(n)=-6*a(n-1)-8*a(n-2)+ 2*a(n-3)+ a(n-4). - _Harvey P. Dale_, May 23 2015

%t CoefficientList[Series[-(1+x^2)/((x^2+4x+1)(x^2-2x-1)),{x,0,40}],x] (* or *) LinearRecurrence[{-6,-8,2,1},{1,-6,29,-124},40] (* _Harvey P. Dale_, May 23 2015 *)

%o Floretion Algebra Multiplication Program, FAMP Code: 1basejseq[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

%Y Cf. A111639, A111640, A111641, A111642, A111643, A111645, A000126.

%K easy,sign

%O 0,2

%A _Creighton Dement_, Aug 10 2005

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Last modified June 23 22:56 EDT 2021. Contains 345402 sequences. (Running on oeis4.)