A083594 a(n) = (7 - 4*(-2)^n)/3.

1, 5, -3, 13, -19, 45, -83, 173, -339, 685, -1363, 2733, -5459, 10925, -21843, 43693, -87379, 174765, -349523, 699053, -1398099, 2796205, -5592403, 11184813, -22369619, 44739245, -89478483, 178956973, -357913939, 715827885, -1431655763, 2863311533, -5726623059

Offset: 0

Author

Paul Barry, May 02 2003

Keywords

• easy
• sign

Comments

Also generalized k-bonacci sequence a(n)=2*a(n-2)-a(n-1). - Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 30 2007

Links

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

Crossrefs

Cf. A083595.

Programs

Mathematica

(7-4(-2)^Range[0,40])/3 (* or *) LinearRecurrence[{-1,2},{1,5},40] (* Harvey P. Dale, Feb 25 2012 *)

Formula

G.f.: (1+6*x)/((1-x)*(1+2*x)).

E.g.f.: (7*exp(x)-4*exp(-2*x))/3.