A168642 a(n) = (8*2^n + (-1)^n)/3 for n > 0; a(0) = 1.

1, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, 715827883, 1431655765, 2863311531

Offset

0,2

Comments

First differences of A085278.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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

Formula

a(n) = A001045(n+3) for n > 0.

a(n) = a(n-1) + 2*a(n-2) for n > 2; a(0) = 1, a(1) = 5, a(2) = 11.

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

E.g.f.: (8*exp(2*x) - 6 + exp(-x))/3. - G. C. Greubel, Jul 28 2016

Mathematica

Table[(8*2^n +(-1)^n)/3 - 2*Boole[n==0], {n, 0, 40}] (* or *) LinearRecurrence[{1, 2}, {1, 5, 11}, 40] (* G. C. Greubel, Jul 28 2016; Feb 05 2021 *)

Prog

(Magma) [1] cat [ (8*2^n+(-1)^n)/3: n in [1..30] ];
(PARI) a(n)=([0, 1; 2, 1]^n*[1; 5])[1, 1] \\ Charles R Greathouse IV, Jul 29 2016
(Sage) [1]+[(2^(n+3) +(-1)^n)/3 for n in (1..40)] # G. C. Greubel, Feb 05 2021

Crossrefs

Cf. A001045 (Jacobsthal sequence), A085278 (expansion of (1+2*x)^2/((1-2*x)*(1-x^2))).

Sequence in context: A166863 A163704 A131898 * A357750 A234597 A261982

Adjacent sequences: A168639 A168640 A168641 * A168643 A168644 A168645

Keyword

nonn,easy

Author

Klaus Brockhaus, Dec 01 2009

Status

approved