cp's OEIS Frontend

A321309 Coefficients of the power series expansion at p=1 of the growth rate C(p) of the length of the longest increasing path in an Erdös-Rényi graph with edge probability p.

%I A321309 #34 Jun 24 2024 12:26:33
%S A321309 1,1,1,3,7,15,29,54,102,197,375,687,1226,2182,3885,6828,11767,19971,
%T A321309 33519,55525,90293,143350,221149,329472,467362,611441,683794,487644,
%U A321309 -425932,-3026915,-9327152,-23364105,-53026834,-113415526,-232986460,-464621237,-905199293
%N A321309 Coefficients of the power series expansion at p=1 of the growth rate C(p) of the length of the longest increasing path in an Erdös-Rényi graph with edge probability p.
%C A321309 The entries are known to be integers, they were conjectured to be nonnegative and increasing starting from index 2. The radius of convergence of the generating function is at least (sqrt(2)-1)/2 and at most 1.
%C A321309 C(p) is also the speed of the front of the infinite-bin model with moves following a geometric distribution of parameter p.
%H A321309 Benjamin Terlat, <a href="/A321309/b321309.txt">Table of n, a(n) for n = 0..44</a>
%H A321309 Sergey Foss and Takis Konstantopoulos, <a href="https://www.researchgate.net/publication/2834708_Extended_Renovation_Theory_and_Limit_Theorems_for_Stochastic_Ordered_Graphs">Extended renovation theory and limit theorems for stochastic ordered graphs</a>, Markov Process and Related Fields, 9-3 (2003), 413-468.
%H A321309 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. See page 30.
%H A321309 B. Mallein and S. Ramassamy, <a href="http://arxiv.org/abs/1610.04043">Barak-Erdös graphs and the infinite-bin model</a>, arXiv:1610.04043 [math.PR], 2016.
%e A321309 C(1+x) = 1 + x + x^2 + 3x^3 + 7x^4 + 15x^5 + ...
%Y A321309 Cf. A373089, A373090, A373091.
%K A321309 sign
%O A321309 0,4
%A A321309 _Sanjay Ramassamy_, Nov 03 2018
%E A321309 a(17)-a(20) from Bastien Mallein added by _Stefano Spezia_, Dec 20 2023
%E A321309 a(21) and beyond from _Benjamin Terlat_, Jun 24 2024