

A349990


For any n >= 0, consider a sandpile model on the infinite square 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.


5



0, 1, 1, 1, 4, 5, 5, 5, 4, 5, 5, 5, 4, 5, 5, 5, 12, 13, 13, 13, 12, 13, 13, 13, 12, 13, 13, 13, 16, 17, 17, 17, 20, 21, 21, 21, 20, 21, 21, 21, 20, 21, 21, 21, 24, 25, 25, 25, 24, 25, 25, 25, 24, 25, 25, 25, 32, 33, 33, 33, 36, 37, 37, 37, 36, 37, 37, 37, 36
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OFFSET

0,5


COMMENTS

A site is unstable when it holds 4 or more grains.
As long as there is an unstable site:
 choose such an unstable site,
 remove 4 grains from this site and add 1 grain to each of its four 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



FORMULA

a(4*n) + 1 = a(4*n+1) = a(4*n+2) = a(4*n+3).


EXAMPLE

For n = 25:
 after stabilization, we have the following configuration:
1
2 3 2
1 3 1 3 1
2 3 2
1
 there are 13 nonempty sites,
 so a(25) = 13.


PROG

(C++) See Links section.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



