The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A370825 a(n) is the numerator of the ratio of winning probabilities in a game similar to A370823, but with a draw and single round odds A:B:draw of 3:2:1. 3
 3, 2, 39, 4, 363, 26, 3279, 328, 29523, 1342, 11553, 292, 2391483, 1195742, 21523359, 126608, 193710243, 728234, 1743392199, 3169804, 15690529803, 341098474, 3004569537, 155181064, 1270932914163, 635466457082, 11438396227479, 39442745612, 102945566047323, 21563796826 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Such a game can be implemented, for instance, by rolling a single die per round, with A winning the round on numbers 1, 2, 3, B winning on 4, 5 and a draw on 6. To win the game it is necessary to win n rounds in a row. The draw also terminates winning streaks of A or B. LINKS Paolo Xausa, Table of n, a(n) for n = 1..2000 FORMULA a(n)/A370826(n) = (3/4) * (3^n - 1) / (2^n - 1). EXAMPLE a(n)/A370826(n) for n=1..14: 3/2, 2, 39/14, 4, 363/62, 26/3, 3279/254, 328/17, 29523/1022, 1342/31, 11553/178, 292/3, 2391483/16382, 1195742/5461. MATHEMATICA Array[Numerator[3/4*(3^#-1)/(2^#-1)] &, 50] (* Paolo Xausa, Mar 11 2024 *) PROG (PARI) a370825(n) = numerator((3/4) * (3^n - 1) / (2^n - 1)); (Python) from math import gcd def A370825(n): return (a:=3**(n+1)-3>>1)//gcd(a, (1<

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

Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)