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

-5, 121, -2205, 39601, -710645, 12752041, -228826125, 4106118241, -73681302245, 1322157322201, -23725150497405, 425730551631121, -7639424778862805, 137083915467899401, -2459871053643326445, 44140595050111976641, -792070839848372253125

Offset

0,1

Comments

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.

Links

Colin Barker, Table of n, a(n) for n = 0..700

Index entries for linear recurrences with constant coefficients, signature (-19,-19,-1).

Formula

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

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

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

a(n) = -7*(-1)^n*A049660(n+1) +3*(-1)^n*A049660(n) +2*(-1)^n. - R. J. Mathar, Sep 11 2019

Maple

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]

Mathematica

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 *)

Prog

(PARI) Vec(-(5-26*x+x^2)/((1+x)*(1+18*x+x^2)) + O(x^25)) \\ Colin Barker, Mar 04 2016

Crossrefs

Sequence in context: A258978 A128275 A028448 * A282271 A179299 A012179

Adjacent sequences: A108788 A108789 A108790 * A108792 A108793 A108794

Keyword

easy,sign

Author

Creighton Dement, Jul 06 2005

Status

approved