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 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 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=0..68. Rémy Sigrist, Colored representation of the stabilized configuration for n = 1000000 (white, green, purple and gold pixels correspond to sites with 0, 1, 2 and 3 grains, respectively) Rémy Sigrist, C++ program for A349990 Wikipedia, Sandpile models on infinite grids 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 Cf. A307097, A349991. Sequence in context: A360853 A094848 A308740 * A117768 A018245 A264936 Adjacent sequences: A349987 A349988 A349989 * A349991 A349992 A349993 KEYWORD nonn AUTHOR Rémy Sigrist, Dec 08 2021 STATUS approved

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)