cp's OEIS Frontend

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).

%I A058184 #23 Oct 11 2023 17:04:55
%S A058184 0,0,-1,0,1,2,4,6,7,6,1,-10,-28,-52,-77,-92,-79,-14,128,362,675,1002,
%T A058184 1201,1038,200,-1640,-4681,-8760,-13039,-15678,-13636,-2834,21007,
%U A058184 60526,113681,169670,204652,179108,39883,-269012,-782559,-1475214,-2207752,-2671278
%N 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).
%H A058184 Alois P. Heinz, <a href="/A058184/b058184.txt">Table of n, a(n) for n = 0..1000</a>
%H A058184 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,-1).
%F A058184 a(n) = a(n-1)-A014291(n-2) = 2*a(n-1)-a(n-2)-a(n-4).
%F A058184 G.f.: (2*x^3-x^2)/(1-2*x+x^2+x^4). - _Alois P. Heinz_, Sep 24 2008
%p A058184 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
%t A058184 CoefficientList[Series[(2x^3-x^2)/(1-2x+x^2+x^4),{x,0,50}],x]  (* _Harvey P. Dale_, Apr 03 2011 *)
%o A058184 (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
%Y A058184 Cf. A014291.
%K A058184 sign,nice,easy
%O A058184 0,6
%A A058184 _Henry Bottomley_, Dec 04 2000