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A111642 Expansion of 2*(x-1)*(x+1)/((x^2+4*x+1)*(x^2-2*x-1)). 7

%I #10 Mar 11 2024 03:48:12

%S 2,-12,54,-224,890,-3452,13198,-50016,188498,-707916,2652678,-9925760,

%T 37105802,-138631292,517742494,-1933118784,7216615970,-26937891852,

%U 100545928278,-375272321696,1400607336218,-5227311479036,19509011469358,-72809634633120,271731700422002

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

%C Floretion Algebra Multiplication Program, FAMP Code: 1ibaseseq[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

%H Colin Barker, <a href="/A111642/b111642.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

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

%Y Cf. A111639, A111640, A111641, A111643, A111644, A000126.

%K easy,sign

%O 0,1

%A _Creighton Dement_, Aug 10 2005

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Last modified March 28 15:28 EDT 2024. Contains 371254 sequences. (Running on oeis4.)