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%I #12 Mar 11 2024 03:48:29
%S -2,8,-34,136,-530,2032,-7714,29104,-109378,410040,-1534722,5738360,
%T -21441682,80083808,-299027394,1116348896,-4167148290,15554127592,
%U -58053908834,216672484584,-808662529938,3018041612880,-11263658377442,42036964786320,-156885101002562
%N Expansion of 2*(x+1)^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].
%C Floretion Algebra Multiplication Program, FAMP Code: 1baseiseq[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="/A111643/b111643.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 From _Colin Barker_, May 01 2019: (Start)
%F a(n) = (-3*(-1-sqrt(2))^(1+n) - 3*(-1+sqrt(2))^(1+n) - 9*(-2-sqrt(3))^n - 5*sqrt(3)*(-2-sqrt(3))^n - 9*(-2+sqrt(3))^n + 5*sqrt(3)*(-2+sqrt(3))^n) / 6.
%F a(n) = -6*a(n-1) - 8*a(n-2) + 2*a(n-3) + a(n-4) for n>3.
%F (End)
%o (PARI) Vec(-2*(1 + x)^2 / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^40)) \\ _Colin Barker_, May 01 2019
%Y Cf. A111639, A111640, A111641, A111642, A111644, A000126.
%K easy,sign
%O 0,1
%A _Creighton Dement_, Aug 10 2005
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