%I A060747
%S A060747 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,
%T A060747 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,
%U A060747 111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,
               147,149,151
%V A060747 -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,
%W A060747 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,
%X A060747 111,113,115,117,119,121,123,125,127,129,131,133,135,137,139,141,143,145,
               147,149,151
%N A060747 2n-1.
%C A060747 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.
%C A060747 abs(a(n))=2n-1+2*0^n. It has A048495 as binomial transform. - Paul Barry 
               (pbarry(AT)wit.ie), Jun 09 2003
%H A060747 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A060747 a(n) =A005408(n)-2 =A005843(n)-1 =-A000984(n)/A002420(n) =A001477(n)+A023443(n). 
               G.f.: (3x-1)/(1-x)^2.
%F A060747 Abs(a(n))=sum{k=0..n, mod(A078008(k), 4)}. - Paul Barry (pbarry(AT)wit.ie), 
               Mar 12 2004
%F A060747 E.g.f.: exp(x)*(2x-1); - Paul Barry (pbarry(AT)wit.ie), Mar 31 2007
%F A060747 a(n)=2*a(n-1)-a(n-2); a(0)=-1, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%F A060747 a(n)=4*n-a(n-1)-8 (with a(1)=-1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 22 2009]
%e A060747 For n=2, a(2)=4*2+1-8=1; n=3, a(3)=4*3-1-8=3; n=4, a(4)=4*4-3-8=5 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 22 2009]
%Y A060747 Sequence in context: A004273 A005408 A144396 this_sequence A089684 A105356 
               A082453
%Y A060747 Adjacent sequences: A060744 A060745 A060746 this_sequence A060748 A060749 
               A060750
%K A060747 easy,sign,new
%O A060747 0,3
%A A060747 Henry Bottomley (se16(AT)btinternet.com), Apr 26 2001