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A373091
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.
4
1, 1, 1, 3, 7, 15, 29, 54, 102, 197, 375, 687, 1226, 2182, 3885, 6827, 11757, 19920, 33339, 55012, 88980, 140141, 213535, 311997, 428578, 527659, 506451, 118728, -1180673, -4546846, -12344870, -29279209, -64481947, -135339292, -274463246, -542210697, -1048748528, -1992459450
OFFSET
0,4
COMMENTS
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.
The first 15 coefficients of this sequence coincide with the first 15 coefficients of A321309.
LINKS
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Last passage percolation and limit theorems in Barak-Erdős directed random graphs and related models, arXiv:2312.02884 [math.PR], 2023.
Sergey Foss, Takis Konstantopoulos, Bastien Mallein, and Sanjay Ramassamy, Estimation of the last passage percolation constant in a charged complete directed acyclic graph via perfect simulation, arXiv:2110.01559 [math.PR], 2023.
EXAMPLE
C(-3,x) = 1 + x + x^2 + 3*x^3 + 7*x^4 + 15*x^5 + ...
CROSSREFS
KEYWORD
sign
AUTHOR
Benjamin Terlat, May 23 2024
STATUS
approved