

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
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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



KEYWORD

nonn


AUTHOR



STATUS

approved



