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 A166872 #24 Jul 01 2019 02:03:59
%S A166872 0,0,0,0,0,0,1,1,1,2,2,2,3,3,3,3,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,10,
%T A166872 10,10,11,11,12,12,12,13,13,14,14,14,15,15,15,16,16,17,17,18,18,18,19,
%U A166872 19,20,20,20,21,21,22,22,22,23,23,24,24,24,25,25,26,26,27,27,27,28,28,29
%N A166872 a(n) = floor(n/2 + 2 - sqrt(17/4 + 2*n)).
%C A166872 Each nonnegative integer k occurs 2 to 6 times in the sequence, with 0 occurring 6 times, 3 occurring 4 times, all others either 2 or 3 times. Conjecture: The sequence of integers k which occur 3 times has the g.f. (1 + 2*x^2 - 2*x^3 + x^6 - x^8 - x^9 + x^11)/(1 - 2*x + x^2 - x^8 + 2*x^9 - x^10). - _Robert Israel_, May 27 2016
%H A166872 G. C. Greubel, <a href="/A166872/b166872.txt">Table of n, a(n) for n = 1..1000</a>
%H A166872 Matthieu Latapy, Roberto Mantaci, Michel Morvan and Ha Duong Phan, <a href="https://doi.org/10.1016/S0304-3975(00)00363-7">Structure of some sand pile model</a>, Theoretical Computer Science 262 (2001), pp. 525-556.
%F A166872 a(n) = floor(n/2 + 2 - sqrt(17/4 + 2*n)).
%F A166872 a(n) = k iff ceiling(2*k + sqrt(16*k+1)) <= n <= ceiling(2*k + 3 + sqrt(16*k+17)). - _Robert Israel_, May 27 2016
%p A166872 nk:= k -> ceil(2*(k+1)+sqrt(16*k+17)) - ceil(2*k+sqrt(16*k+1)):
%p A166872 seq(k$nk(k), k=0..50); # _Robert Israel_, May 27 2016
%t A166872 Table[Floor[n/2 + 2 - Sqrt[2*n + 17/4]], {n, 1, 100}] (* _G. C. Greubel_, May 27 2016 *)
%Y A166872 Cf. A056219.
%K A166872 nonn
%O A166872 1,10
%A A166872 _Roger L. Bagula_, Oct 22 2009
%E A166872 Edited by the associate editors of the OEIS, Nov 09 2009