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A083943 A generalized Jacobsthal sequence. 2

%I

%S 0,1,-1,-1,-5,-9,-21,-41,-85,-169,-341,-681,-1365,-2729,-5461,-10921,

%T -21845,-43689,-87381,-174761,-349525,-699049,-1398101,-2796201,

%U -5592405,-11184809,-22369621,-44739241,-89478485,-178956969,-357913941,-715827881,-1431655765

%N A generalized Jacobsthal sequence.

%C a(2n)=-A001045(2n), a(2n+1)=2-A001045(2n+1).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).

%F a(n)=1-2^n/3-2(-1)^n/3; a(n)=a(n-1)+2a(n-2)-2, a(0)=0, a(1)=1; G.f.: x(1-3x)/((1+x)(1-x)(1-2x)); E.g.f.: exp(x)-(exp(2x)+2exp(-x))/3.

%t LinearRecurrence[{2,1,-2},{0,1,-1},50] (* _Harvey P. Dale_, Jul 28 2020 *)

%Y Cf. A083944.

%K easy,sign

%O 0,5

%A _Paul Barry_, May 09 2003

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)