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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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)
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Dec 08 2021
STATUS
approved

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Last modified July 13 23:31 EDT 2024. Contains 374290 sequences. (Running on oeis4.)