This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A088804 #15 Aug 06 2024 09:31:25 %S A088804 1,4,8,14,21,29,39,51,63,77,93,110,128,148,170,192,216,242,268,296, %T A088804 326,358,390,424,460,496,534,574,615,657,701,747,793,841,891,941,993, %U A088804 1047,1103,1159,1217,1277,1337,1399,1463,1529,1595,1663,1733,1803,1875,1949 %N A088804 a(n) gives the number of steps taken in a process which manipulates piles of tokens arranged in a line. There are 2n (or 2n+1) tokens in all. Initially they are all in one pile. At each step, from each pile with more than 1 token, one token is taken and added to the pile on its left and one is taken and added to the pile on its right. The redistributions in each step are done in parallel. %H A088804 R. Anderson, L. Lovasz, P. Shor, J. Spencer, E. Tardos, S. Winograd, <a href="http://www.jstor.org/stable/2323970">Disks, balls and walls: analysis of a combinatorial game</a>, Amer. Math. Monthly, 6, 96, pp. 481-493, 1989. %H A088804 Anders Björner, László Lovászb, Peter W. Shor, <a href="http://dx.doi.org/10.1016/S0195-6698(13)80111-4">Chip-firing games on graphs</a>, European Journal of Combinatorics 12, pp. 283-291, 1991. %H A088804 Mikkel Thorup, <a href="https://citeseerx.ist.psu.edu/pdf/0bde8b0492a10db5460c77c55c8370650862189d">Firing Games</a> %F A088804 The sequence is asymptotically quadratic with a(n) ~= c*n^2, where c is between 0.33 and 1, with estimate 0.7078 for n = 1, 000. %e A088804 E.g., a(2) = 4 because there are 4 steps in the process beginning with 4 tokens: %e A088804 0 0 4 0 0 %e A088804 0 1 2 1 0 %e A088804 0 2 0 2 0 %e A088804 1 0 2 0 1 %e A088804 1 1 0 1 1 %Y A088804 Cf. A088803. %K A088804 nonn %O A088804 1,2 %A A088804 _Rob Arthan_, Oct 17 2003