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A108791 a(2n) = -5*(fibonacci(6n+2))^2, a(2n+1) = (lucas(6n+5))^2. 1

%I

%S -5,121,-2205,39601,-710645,12752041,-228826125,4106118241,

%T -73681302245,1322157322201,-23725150497405,425730551631121,

%U -7639424778862805,137083915467899401,-2459871053643326445,44140595050111976641,-792070839848372253125

%N a(2n) = -5*(fibonacci(6n+2))^2, a(2n+1) = (lucas(6n+5))^2.

%C Define the floretions A = + 'i - 'k + i' - k' - 'jj' - 'ij' - 'ji' - 'jk' - 'kj'; B = - 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj'; C = - 'j + 'k - j' + k' - 'ii' - 'ij' - 'ik' - 'ji' - 'ki'. The floretion given in the program code is A*B*C.

%H Colin Barker, <a href="/A108791/b108791.txt">Table of n, a(n) for n = 0..700</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-19,-19,-1).

%F G.f. (-5+26*x-x^2)/((x+1)*(x^2+18*x+1)).

%F a(0)=-5, a(1)=121, a(2)=-2205, a(n) = -19*a(n-1)-19*a(n-2)-a(n-3). - _Harvey P. Dale_, Jan 11 2016

%F a(n) = (2*(-1)^n-1/2*(-9-4*sqrt(5))^(-n)*(7-3*sqrt(5)+(-9-4*sqrt(5))^(2*n)*(7+3*sqrt(5)))). - _Colin Barker_, Mar 04 2016

%F a(n) = -7*(-1)^n*A049660(n+1) +3*(-1)^n*A049660(n) +2*(-1)^n. - _R. J. Mathar_, Sep 11 2019

%p seriestolist(series(-(5-26*x+x^2)/((x+1)*(x^2+18*x+1)),x=0,25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1vesseq[ + 14'i - 2'j - 2'k + 14i' - 2j' - 2k' + 4'ii' - 12'jj' + 12'kk' - 4'ij' - 4'ji' - 8'jk' - 8'kj' - 5e]

%t CoefficientList[Series[(-5+26x-x^2)/((x+1)(x^2+18x+1)),{x,0,20}],x] (* or *) LinearRecurrence[{-19,-19,-1},{-5,121,-2205},20] (* _Harvey P. Dale_, Jan 11 2016 *)

%o (PARI) Vec(-(5-26*x+x^2)/((1+x)*(1+18*x+x^2)) + O(x^25)) \\ _Colin Barker_, Mar 04 2016

%K easy,sign

%O 0,1

%A _Creighton Dement_, Jul 06 2005

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Last modified April 13 14:11 EDT 2021. Contains 342936 sequences. (Running on oeis4.)