A373091 - OEIS

%I #16 Jun 22 2024 18:02:46

%S 1,1,1,3,7,15,29,54,102,197,375,687,1226,2182,3885,6827,11757,19920,

%T 33339,55012,88980,140141,213535,311997,428578,527659,506451,118728,

%U -1180673,-4546846,-12344870,-29279209,-64481947,-135339292,-274463246,-542210697,-1048748528,-1992459450

%N Coefficients of the power series expansion at p=1 of the time constant C(-3,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -3 with respective probabilities p and 1-p.

%C C(-3,p) is also the speed of the front for an interacting particle system with 4 bins, which corresponds to the particular case of the max-growth system where the probability distribution has two atoms 1 and -3 with respective probabilities p and 1-p.

%C The first 15 coefficients of this sequence coincide with the first 15 coefficients of A321309.

%H Benjamin Terlat, <a href="/A373091/b373091.txt">Table of n, a(n) for n = 0..750</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(-3,x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 15*x^5 + ...

%Y Cf. A321309, A373089, A373090.

%K sign

%O 0,4

%A _Benjamin Terlat_, May 23 2024