A373090 - OEIS

%I #19 Jun 22 2024 18:02:10

%S 1,1,1,3,7,15,29,54,102,197,376,695,1260,2286,4155,7489,13347,23621,

%T 41609,72884,126789,218903,375140,638554,1079382,1809256,3003411,

%U 4934260,8013764,12839395,20232603,31228335,46918878,67947178,93185004,116654299,120921410,63471736,-150813354,-723950195

%N Coefficients of the power series expansion at p=1 of the time constant C(-2,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -2 with respective probabilities p and 1-p.

%C C(-2,p) is also the speed of the front for an interacting particle system with 3 bins, which corresponds to the particular case of the max-growth system where the probability distribution has two atoms 1 and -2 with respective probabilities p and 1-p.

%C The first 10 coefficients of this sequence coincide with the first 10 coefficients of A321309.

%H Benjamin Terlat, <a href="/A373090/b373090.txt">Table of n, a(n) for n = 0..1250</a>

%H Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, <a href="https://arxiv.org/abs/2312.02884">Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models</a>, arXiv:2312.02884 [math.PR], 2023.

%H Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, <a href="https://arxiv.org/abs/2110.01559">Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation</a>, arXiv:2110.01559 [math.PR], 2023.

%e C(-2,x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 15*x^5 + ...

%Y Cf. A321309, A373089, A373091.

%K sign

%O 0,4

%A _Benjamin Terlat_, May 23 2024