This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A181784 Numerators of a series sum related to a game of chance. 1
1, 1, 4, 22, 140, 969, 7084, 53820, 420732, 3782992, 32389076, 275617830, 2350749914, 20140518790, 173429992350, 1500850805160, 14550277251918, 133009333771170, 1198324107797254 (list; graph; refs; listen; history; text; internal format)



Consider a 1-dimensional random walk from 0 with equal-probability steps of Pi and -1.  One way to compute the probability of eventually walking below 0 is as the sum over n of the probabilities of becoming negative after a walk with exactly n steps of Pi (n >=0) and max(ceil(n*pi),1) steps of -1.  The total number of walks of such length for a given n is 2^(n+max(ceil(n*pi),1)), or 2^(n+A004084(n)) (n>=1), forming a sequence of denominators, and this sequence gives the numerators, the number of possible sequences of length (n+max(ceil(n*pi),1)) drawn from {Pi, -1} such that no partial sum except the total sum is < 0.

See the Munafo web page for complete description.

a(n) diverges from A002293 because pi is not exactly 3.


Table of n, a(n) for n=0..18.

R. Munafo, Related to a Game of Chance

"My Math Forum" discussion thread, I give, duz... what is it?

"duz" blog entry, Random Walking


Numerators of series sum 1/2 + 1/32 + 4/512 + 22/8192 + 140/131072 + ...


Sequence in context: A216712 A240586 A002293 * A003287 A077056 A227404

Adjacent sequences:  A181781 A181782 A181783 * A181785 A181786 A181787




Robert Munafo, Dec 21 2010


a(18) from Robert Munafo, Dec 22 2010



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 19 02:36 EST 2018. Contains 318245 sequences. (Running on oeis4.)