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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 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

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