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 A350188 #37 Mar 11 2022 07:42:59
%S A350188 0,1,1,3,4,4,3,4,4,7,8,8,10,11,11,10,11,11,14,15,15,17,18,18,17,18,18,
%T A350188 21,22,22,24,25,25,24,25,25,27,28,28,30,31,31,30,31,31,36,37,37,39,40,
%U A350188 40,39,40,40,39,40,40,42,43,43,42,43,43,45,46,46,48,49
%N A350188 Consider a 2D sandpile model where each site with 3 or more grains, say at location (x, y), topples and transfers one grain of sand to the sites at locations (x+1, y-1), (x+1, y) and (x+1, y+1); a(n) gives the number of nonempty sites after stabilization of a configuration starting with n grains at the origin.
%C A350188 Sites containing 0, 1 or 2 grains are stable.
%C A350188 After stabilization, there are:
%C A350188 - 2*a(n) - n sites with one grain,
%C A350188 - n - a(n) sites with two grains.
%H A350188 Rémy Sigrist, <a href="/A350188/b350188.txt">Table of n, a(n) for n = 0..10000</a>
%H A350188 Rémy Sigrist, <a href="/A350188/a350188.png">Representation of the configuration for n = 100000</a> (blue pixels correspond to sites with one grain, red pixels to sites with two grains)
%F A350188 a(3*n) + 1 = a(3*n + 1) = a(3*n + 2).
%e A350188 For n = 10 :
%e A350188 - the model evolves (for example) as follows:
%e A350188 1 1
%e A350188 3 . 2 . 2 1
%e A350188 10 -> 1 3 -> 1 . 3 -> 1 . . 1
%e A350188 3 . 2 . 2 1
%e A350188 1 1
%e A350188 - there are 8 nonempty sites in the stabilized configuration,
%e A350188 - so a(10) = 8.
%o A350188 (PARI) a(n) = { my (s=[n], v=0); for (k=-1, oo, if (vecmax(s)==0, return (v), v += sum(k=1, #s, s[k]%3>0); s \= 3; s = concat([ s , [0], [0]]) + concat([[0], s , [0]]) + concat([[0], [0], s ]); while (#s>2 && s[1]==0, s = s[2..#s-1]))) }
%Y A350188 Cf. A349990, A351783, A352226.
%K A350188 nonn
%O A350188 0,4
%A A350188 _Rémy Sigrist_, Mar 09 2022