A060747 - OEIS

A060747

a(n) = 2*n - 1.

-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 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 hasA048495as 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. SeeA145051andA040001.-Jaroslav Krizek,May 28 2010

FromJaroslav Krizek,May 28 2010: (Start)

For n >= 1, a(n) = corresponding values of antiharmonic means to numbers fromA016777(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.: (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