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A060747 a(n) = 2n-1. 16
-1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141, 143, 145, 147, 149, 151 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

If you put n red balls and n blue balls in a bag and draw them one-by-one without replacement, the probability of never having drawn equal numbers of the two colors before the final ball is drawn is 1/a(n) unsigned.

abs(a(n))=2n-1+2*0^n. It has A048495 as binomial transform. - Paul Barry, Jun 09 2003

For n >= 1, a(n) = numbers k such that arithmetic mean of the first k positive integers is integer. A040001(a(n)) = 1. See A145051 and A040001. -  Jaroslav Krizek, May 28 2010

From Jaroslav Krizek, May 28 2010: (Start)

For n >= 1, a(n) = corresponding values of antiharmonic means to numbers from A016777 (numbers k such that antiharmonic mean of the first k positive integers is integer).

a(n) = A000330(A016777(n)) / A000217(A016777(n)) = A146535(A016777(n)+1). (End)

LINKS

Table of n, a(n) for n=0..76.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

a(n) = A005408(n)-2 = A005843(n)-1 = -A000984(n)/A002420(n) = A001477(n)+A023443(n).

G.f.: (3x-1)/(1-x)^2.

Abs(a(n))=sum{k=0..n, mod(A078008(k), 4)}. - Paul Barry, Mar 12 2004

E.g.f.: exp(x)*(2x-1); - Paul Barry, Mar 31 2007

a(n)=2*a(n-1)-a(n-2); a(0)=-1, a(1)=1. - Philippe Deléham, Nov 03 2008

a(n)=4*n-a(n-1)-4 (with a(0)=-1) - Vincenzo Librandi, Aug 07 2010

EXAMPLE

a(1) = 4*1+1-4 = 1; a(2) = 4*2-1-4 = 3; a(3) = 4*3-3-4 = 5; a(4) = 4*4-5-4 = 7 - Vincenzo Librandi, Aug 07 2010

MATHEMATICA

Table[2*n - 1, {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)

PROG

(Haskell)

a060747 = subtract 1 . (* 2)

a060747_list = [-1, 1 ..] -- Reinhard Zumkeller, Jul 05 2015

-- Reinhard Zumkeller, Jul 05 2015

(PARI) a(n)=2*n-1 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Sequence in context: A005408 A176271 A144396 * A089684 A283002 A105356

Adjacent sequences:  A060744 A060745 A060746 * A060748 A060749 A060750

KEYWORD

easy,sign

AUTHOR

Henry Bottomley, Apr 26 2001

STATUS

approved

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Last modified April 29 09:07 EDT 2017. Contains 285604 sequences.