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A006589 a(n) = (n+3)*2^n-1. 5
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

Table of n, a(n) for n=-1..25.

M. Le Brun, Email to N. J. A. Sloane, Jul 1991

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

FORMULA

G.f.: (2-3x)/((1-x)(1-2x)^2). a(n)=5*a(n-1)-8*a(n-2)+4*a(n-3). - R. J. Mathar, Jan 25 2009

a(n) = A001792(n+1)-1. - R. J. Mathar, Aug 03 2015

a(n) = Sum_{k=0..n} Sum_{i=0..n} C(n,i) + C(k,i). - Wesley Ivan Hurt, Sep 21 2017

PROG

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

CROSSREFS

Cf. A001792, A045623.

Sequence in context: A110299 A209400 A112304 * A238914 A227946 A099484

Adjacent sequences:  A006586 A006587 A006588 * A006590 A006591 A006592

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 23 21:01 EDT 2018. Contains 316541 sequences. (Running on oeis4.)