login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006589 a(n) = (n+3)*2^n - 1. 6
0, 2, 7, 19, 47, 111, 255, 575, 1279, 2815, 6143, 13311, 28671, 61439, 131071, 278527, 589823, 1245183, 2621439, 5505023, 11534335, 24117247, 50331647, 104857599, 218103807, 452984831, 939524095 (list; graph; refs; listen; history; text; internal format)
OFFSET
-1,2
COMMENTS
Binomial transform of [2/1, 3/2, 4/3, 5/4, ...] = 2/1, 7/2, 19/3, 47/4, 111/5, ... - Gary W. Adamson, Apr 28 2005
Binomial transform of A087156 := [0,2,3,4,5,6,7,8,9,10,...]. - Philippe Deléham, Nov 25 2008
Partial sums of A045623 minus 1. - R. J. Mathar, Jan 25 2009
For n >= 0: sums of rows of the triangle in A173786. - Reinhard Zumkeller, Feb 28 2010
REFERENCES
W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 28.
LINKS
FORMULA
From R. J. Mathar, Jan 25 2009: (Start)
G.f.: (2-3*x)/((1-x)*(1-2*x)^2).
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). (End)
a(n) = A001792(n+1) - 1. - R. J. Mathar, Aug 03 2015
a(n) = Sum_{k=0..n} Sum_{i=0..n} (binomial(n,i) + binomial(k,i)). - Wesley Ivan Hurt, Sep 21 2017
E.g.f.: (3 + 2*x)*exp(2*x) - exp(x). - G. C. Greubel, Jul 07 2021
MATHEMATICA
Table[2^n*(n+3) -1, {n, -1, 30}] (* G. C. Greubel, Jul 07 2021 *)
PROG
(PARI) a(n)=(n+3)*2^n-1 \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [2^n*(n+3) -1 for n in (-1..30)] # G. C. Greubel, Jul 07 2021
CROSSREFS
Sequence in context: A110299 A209400 A112304 * A238914 A227946 A328990
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)