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, 6442450912, 12884901855

Offset: 1

Author

Klaus Brockhaus, Oct 09 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A007283.

Programs

Magma

[2^n + 2^(n-1) - n: n in [1..40] ]; // Vincenzo Librandi, May 18 2011

Mathematica

Table[2^n + 2^(n-1) - n, {n,1,50}] (* G. C. Greubel, Oct 26 2017 *)

PARI

for(n=1,31,print1(2^n+2^(n-1)-n,","))

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