A373089 Coefficients of the power series expansion at p=1 of the time constant C(-1,p) for last passage percolation on the complete directed acyclic graph, where the edges' weights are equal to 1 or -1 with respective probabilities p and 1-p.

1, 1, 1, 3, 7, 15, 30, 60, 123, 254, 517, 1040, 2093, 4226, 8523, 17146, 34469, 69295, 139263, 279803, 562076, 1128834, 2266768, 4551848, 9139963, 18350850, 36842933, 73969425, 148503840, 298134233, 598527760, 1201583460, 2412228147, 4842626698, 9721723262, 19516574603

Offset

0,4

Comments

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

The first 6 coefficients of this sequence coincide with the first 6 coefficients of A321309.

Links

Benjamin Terlat, Table of n, a(n) for n = 0..1000

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

Crossrefs

Cf. A321309, A373090, A373091.

Sequence in context: A120411 A350606 A224520 * A291754 A336685 A069112

Adjacent sequences: A373086 A373087 A373088 * A373090 A373091 A373092

Keyword

nonn

Author

Benjamin Terlat, May 23 2024

Status

approved