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.

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

Benjamin Terlat, Table of n, a(n) for n = 0..750

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

Cf. A321309, A373089, A373090.

Sequence in context: A182717 A122768 A344743 * A321309 A373090 A023608

Adjacent sequences: A373088 A373089 A373090 * A373092 A373093 A373094

Keyword

sign

Author

Benjamin Terlat, May 23 2024

Status

approved