cp's OEIS Frontend

A351784 Number of cells containing one or more grains of sand after n grains of sand are added to one cell in an initially empty and infinite 3D cubic grid for the 3D sandpile model.

%I A351784 #23 Mar 06 2022 09:03:31
%S A351784 0,1,1,1,1,1,6,7,7,7,7,7,6,7,7,7,7,7,6,7,7,7,7,7,6,7,7,7,7,7,6,7,7,7,
%T A351784 7,7,24,25,25,25,25,25,24,25,25,25,25,25,24,25,25,25,25,25,24,25,25,
%U A351784 25,25,25,24,25,25,25,25,25,24,25,25,25,25,25,24,25,25,25,25,25,24,25,25
%N A351784 Number of cells containing one or more grains of sand after n grains of sand are added to one cell in an initially empty and infinite 3D cubic grid for the 3D sandpile model.
%C A351784 The 3D sandpile model follows the same rules as the 2D model except that cells topple and transfer one grain of sand to their six nearest neighbors when the cell contains 6 or more grains. Cells containing 0 to 5 grains are stable.
%H A351784 Scott R. Shannon, <a href="/A351784/b351784.txt">Table of n, a(n) for n = 0..10000</a>
%H A351784 Per Bak, Chao Tang, and Kurt Wiesenfeld, <a href="https://doi.org/10.1103/PhysRevLett.59.381">Self-organized criticality: An explanation of the 1/f noise</a>, Phys. Rev. Lett. 59 (1987), 381-384.
%H A351784 Laura Florescu, Daniela Morar, David Perkinson, Nicholas Salter, and Tianyuan Xu, <a href="https://doi.org/10.37236/4472">Sandpiles and Dominos</a>, Electronic Journal of Combinatorics, Volume 22(1), 2015.
%H A351784 Luis David Garcia-Puente and Brady Haran, <a href="https://youtu.be/1MtEUErz7Gg">Sandpiles</a>, Numberphile video, YouTube.com, Jan. 13, 2017.
%H A351784 Zach J. Shannon, <a href="/A351784/a351784.png">Image of the occupied cells for a(96)=44, bisected along the y-z plane</a>. The colors are red=1 (24 total cells), blue=3 (14 total cells), violet=5 (6 total cells) grains per cell.
%Y A351784 Cf. A351783, A351379, A349990 (2D version), A307652, A259013, A180230.
%K A351784 nonn
%O A351784 0,7
%A A351784 _Scott R. Shannon_ and _Zach J. Shannon_, Feb 19 2022