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).
LINKS
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: (3*x - 1)/(1 - x)^2.
Abs(a(n)) = Sum_{k=0..n} (A078008(k) mod 4). - Paul Barry, Mar 12 2004
E.g.f.: exp(x)*(2*x-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 for n>0, with a(0)=-1. - Vincenzo Librandi, Aug 07 2010
MATHEMATICA
Table[2*n - 1, {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2012 *)
LinearRecurrence[{2, -1}, {-1, 1}, 80] (* Harvey P. Dale, Mar 27 2020 *)
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
KEYWORD
sign,easy
AUTHOR
Henry Bottomley, Apr 26 2001
STATUS
approved