A083943 A generalized Jacobsthal sequence.

0, 1, -1, -1, -5, -9, -21, -41, -85, -169, -341, -681, -1365, -2729, -5461, -10921, -21845, -43689, -87381, -174761, -349525, -699049, -1398101, -2796201, -5592405, -11184809, -22369621, -44739241, -89478485, -178956969, -357913941, -715827881, -1431655765

Offset: 0

Author

Paul Barry, May 09 2003

Keywords

• easy
• sign

Comments

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

Links

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

Crossrefs

Cf. A083944.

Programs

Mathematica

LinearRecurrence[{2,1,-2},{0,1,-1},50] (* Harvey P. Dale, Jul 28 2020 *)

Formula

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.