A123720 a(n) = 2^n + 2^(n-1) - n.

2, 4, 9, 20, 43, 90, 185, 376, 759, 1526, 3061, 6132, 12275, 24562, 49137, 98288, 196591, 393198, 786413, 1572844, 3145707, 6291434, 12582889, 25165800, 50331623, 100663270, 201326565, 402653156, 805306339, 1610612706, 3221225441

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Formula

a(n) = A007283(n-1) - n.

O.g.f.: x(2 - 4x + 3x^2)/((1-x)^2*(1-2x)). - R. J. Mathar, Jun 08 2008

E.g.f.: (1/2)*(-3 - 2*x*exp(x) + 3*exp(2*x)). - G. C. Greubel, Oct 26 2017

Mathematica

lst={}; Do[AppendTo[lst, 2^n+2^(n-1)-n], {n, 5!}]; lst (* and/or *) s=2; lst={s}; Do[s+=s+n++; AppendTo[lst, s], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)
Table[2^n + 2^{n-1) - n, {n, 1, 50}] (* or *) LinearRecurrence[{4, -5, 2}, {2, 4, 9}, 50] (* G. C. Greubel, Oct 26 2017 *)

Prog

(PARI) for(n=1, 31, print1(2^n+2^(n-1)-n, ", "))
(Magma) [2^n + 2^(n-1) - n: n in [1..40] ]; // Vincenzo Librandi, May 18 2011

Crossrefs

Cf. A007283.

Sequence in context: A018103 A350092 A175104 * A179744 A266930 A034007

Adjacent sequences: A123717 A123718 A123719 * A123721 A123722 A123723

Keyword

nonn

Author

Klaus Brockhaus, Oct 09 2006

Status

approved