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Search: id:A060747
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| -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; listen)
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OFFSET
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0,3
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COMMENT
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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 (pbarry(AT)wit.ie), Jun 09 2003
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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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 (pbarry(AT)wit.ie), Mar 12 2004
E.g.f.: exp(x)*(2x-1); - Paul Barry (pbarry(AT)wit.ie), Mar 31 2007
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]
a(n)=4*n-a(n-1)-8 (with a(1)=-1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 22 2009]
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EXAMPLE
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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]
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CROSSREFS
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Sequence in context: A004273 A005408 A144396 this_sequence A089684 A105356 A082453
Adjacent sequences: A060744 A060745 A060746 this_sequence A060748 A060749 A060750
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KEYWORD
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easy,sign,new
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 26 2001
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