A058184 "Real rabbits": a(n) = Re(c(n)) where complex c(n) = a(n) + i*b(n) and c(0) = i, c(1) = -i, c(n) = c(n-1) + i*c(n-2).

0, 0, -1, 0, 1, 2, 4, 6, 7, 6, 1, -10, -28, -52, -77, -92, -79, -14, 128, 362, 675, 1002, 1201, 1038, 200, -1640, -4681, -8760, -13039, -15678, -13636, -2834, 21007, 60526, 113681, 169670, 204652, 179108, 39883, -269012, -782559, -1475214, -2207752, -2671278

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,-1).

Formula

a(n) = a(n-1)-A014291(n-2) = 2*a(n-1)-a(n-2)-a(n-4).

G.f.: (2*x^3-x^2)/(1-2*x+x^2+x^4). - Alois P. Heinz, Sep 24 2008

Maple

a:= n-> (Matrix([[0, -1, 0, 0]]). Matrix([[2, 1, 0, 0], [ -1, 0, 1, 0], [0, 0, 0, 1], [ -1, 0, 0, 0]])^n)[1, 4]: seq (a (n), n=0..50); # Alois P. Heinz, Sep 24 2008

Mathematica

CoefficientList[Series[(2x^3-x^2)/(1-2x+x^2+x^4), {x, 0, 50}], x]  (* Harvey P. Dale, Apr 03 2011 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, -1, 2]^n*[0; 0; -1; 0])[1, 1] \\ Charles R Greathouse IV, Jun 16 2015

Crossrefs

Cf. A014291.

Sequence in context: A272665 A114431 A167689 * A087777 A030118 A331379

Adjacent sequences: A058181 A058182 A058183 * A058185 A058186 A058187

Keyword

sign,nice,easy

Author

Henry Bottomley, Dec 04 2000

Status

approved