A083582 a(n) = (8*2^n-5*(-1)^n)/3.

1, 7, 9, 23, 41, 87, 169, 343, 681, 1367, 2729, 5463, 10921, 21847, 43689, 87383, 174761, 349527, 699049, 1398103, 2796201, 5592407, 11184809, 22369623, 44739241, 89478487, 178956969, 357913943, 715827881, 1431655767, 2863311529

Offset: 0

Author

Paul Barry, May 01 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A083581.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Crossrefs

Cf. A140966.

Programs

Magma

[(8*2^n-5*(-1)^n)/3: n in [0..30]]; // Vincenzo Librandi, Aug 13 2011

Maple

BB := n->if n=1 then 3; > elif n=2 then 1; > else 2*BB(n-2)+BB(n-1); > fi: > L:=[]: for k from 2 to 32 do L:=[op(L),BB(k)]: od: L; # Zerinvary Lajos, Mar 19 2007

Mathematica

f[n_]:=2/(n+1);x=6;Table[x=f[x];Denominator[x],{n,0,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2010 *)
LinearRecurrence[{1,2},{1,7},40] (* Harvey P. Dale, May 28 2017 *)

PARI

a(n)=(8*2^n-5*(-1)^n)/3 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = (8*2^n-5(-1)^n)/3.

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

E.g.f.: (8*exp(2*x)-5*exp(-x))/3.

a(n) = 6*A001045(n) + A001045(n+1). - Creighton Dement, Mar 25 2005

a(n) = 2^(n+2)th coefficient of - eta(z)^3 eta(z^5) eta(z^10)^2 /eta(z^2)^2. - Kok Seng Chua (chuaks(AT)ihpc.a-star.edu.sg), Aug 30 2005

a(n) = a(n-1)+2*a(n-2). a(n)+a(n+1) = 8*A000079 = a(n+2)-a(n). - Paul Curtz, Jul 27 2008