A373090 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.

1, 1, 1, 3, 7, 15, 29, 54, 102, 197, 376, 695, 1260, 2286, 4155, 7489, 13347, 23621, 41609, 72884, 126789, 218903, 375140, 638554, 1079382, 1809256, 3003411, 4934260, 8013764, 12839395, 20232603, 31228335, 46918878, 67947178, 93185004, 116654299, 120921410, 63471736, -150813354, -723950195

Offset: 0

Author

Benjamin Terlat, May 23 2024

Keywords

• sign

Comments

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.

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

Examples

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

Links

• Benjamin Terlat, Table of n, a(n) for n = 0..1250
• 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.

Crossrefs

Cf. A321309, A373089, A373091.