



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
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OFFSET

0,3


COMMENTS

If you put n red balls and n blue balls in a bag and draw them onebyone 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))=2n1+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.: (3x1)/(1x)^2.
Abs(a(n))=sum{k=0..n, mod(A078008(k), 4)}.  Paul Barry, Mar 12 2004
E.g.f.: exp(x)*(2x1);  Paul Barry, Mar 31 2007
a(n)=2*a(n1)a(n2); a(0)=1, a(1)=1.  Philippe Deléham, Nov 03 2008
a(n)=4*na(n1)4 (with a(0)=1)  Vincenzo Librandi, Aug 07 2010


EXAMPLE

a(1) = 4*1+14 = 1; a(2) = 4*214 = 3; a(3) = 4*334 = 5; a(4) = 4*454 = 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*n1 \\ 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



