cp's OEIS Frontend

A351783 Number of grains of sand required to be added to one cell at the origin in an initially empty and infinite 3D cubic grid for the 3D sandpile model such that the distance from the origin of the furthest nonempty cell along the axes is n.

%I A351783 #26 Jan 04 2025 13:47:55
%S A351783 0,6,36,162,516,1230,2430,3756,5862,9036,12822,16710,22182,28758,
%T A351783 36144,45444,54966,66270,78870,93834,109866,127260,146412,169698,
%U A351783 192366,218214,244752,273480,307224,341430,380988,420558,463350,510024,558090,611088,664494,723060,784014,844134,921486
%N A351783 Number of grains of sand required to be added to one cell at the origin in an initially empty and infinite 3D cubic grid for the 3D sandpile model such that the distance from the origin of the furthest nonempty cell along the axes is n.
%C A351783 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 A351783 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 A351783 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 A351783 Luis David Garcia-Puente and Brady Haran, <a href="https://youtu.be/1MtEUErz7Gg">Sandpiles</a>, Numberphile video, YouTube.com, Jan. 13, 2017.
%H A351783 Zach J. Shannon, <a href="/A351783/a351783.png">Image of the occupied cells for a(40)=921486</a>. For this and the below image, red=1, green=2, blue=3, violet=4, orange=5 grains per cell. The axes are in the middle of the red squares.
%H A351783 Zach J. Shannon, <a href="/A351783/a351783_1.png">Image of the occupied cells for a(40)=921486, bisected along the y-z plane</a>.
%Y A351783 Cf. A351784, A351379, A307652, A259013, A180230.
%K A351783 nonn
%O A351783 0,2
%A A351783 _Scott R. Shannon_ and _Zach J. Shannon_, Feb 19 2022