A349991 For any n >= 0, consider a sandpile model on the infinite hexagonal lattice starting with n grains at the origin, the other sites being empty; a(n) gives the number of nonempty sites after stabilization of this sandpile model.

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, 7, 7, 18, 19, 19, 19, 19, 19, 18, 19, 19, 19, 19, 19, 18, 19, 19, 19, 19, 19, 18, 19, 19, 19, 19, 19, 18, 19, 19, 19, 19, 19, 18, 19, 19, 19, 19, 19, 24, 25

Offset

0,7

Comments

A site is unstable when it holds 6 or more grains.

As long as there is an unstable site:

- choose such an unstable site,

- remove 6 grains from this site and add 1 grain to each of its six neighbors.

This procedure is guaranteed to result in a stable configuration, which does not depend on the order in which we treat the unstable sites.

Links

Table of n, a(n) for n=0..73.

Rémy Sigrist, Colored representation of the stabilized configuration for n = 1000000 (white, green, purple, gold, blue and red pixels correspond to sites with 0, 1, 2, 3, 4 and 5 grains, respectively)

Rémy Sigrist, C++ program for A349991

Wikipedia, Sandpile models on infinite grids

Formula

a(6*n) + 1 = a(6*n + k) for k = 1..5.

Example

For n = 54:
- after stabilization, we have the following configuration:
             2
          4     4
       2     3     2
          3     3
       4           4
          3     3
       2     3     2
          4     4
             2
- we have 18 nonnempty sites,
- so a(54) = 18.

Prog

(C++) See Links section.

Crossrefs

Cf. A349990.

Sequence in context: A197692 A322415 A023409 * A351784 A008938 A256425

Adjacent sequences: A349988 A349989 A349990 * A349992 A349993 A349994

Keyword

nonn

Author

Rémy Sigrist, Dec 08 2021

Status

approved