A111639 - OEIS

%I #22 Mar 09 2024 14:53:30

%S -3,10,-33,114,-403,1450,-5281,19394,-71619,265450,-986241,3670002,

%T -13670803,50957770,-190026433,708824834,-2644492803,9867263050,

%U -36820012641,137401810674,-512760729619,1913577130090,-7141393334881,26651623320002,-99464199710403

%N Expansion of (3+8*x-3*x^2-2*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].

%C Floretion Algebra Multiplication Program, FAMP Code: 2tesseq[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="/A111639/b111639.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 11 2019: (Start)

%F a(n) = ((-1-sqrt(2))^(1+n) + (-1+sqrt(2))^(1+n) - 2*(-2-sqrt(3))^n - sqrt(3)*(-2-sqrt(3))^n - 2*(-2+sqrt(3))^n + sqrt(3)*(-2+sqrt(3))^n) / 2.

%F a(n) = -6*a(n-1) - 8*a(n-2) + 2*a(n-3) + a(n-4) for n>3. (End)

%t LinearRecurrence[{-6,-8,2,1},{-3,10,-33,114},30] (* _Harvey P. Dale_, Jul 04 2019 *)

%o (PARI) Vec(-(3 + 8*x - 3*x^2 - 2*x^3) / ((1 + 2*x - x^2)*(1 + 4*x + x^2)) + O(x^25)) \\ _Colin Barker_, May 11 2019

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

%K easy,sign

%O 0,1

%A _Creighton Dement_, Aug 10 2005