The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A350188 Consider a 2D sandpile model where each site with 3 or more grains, say at location (x, y), topples and transfers one grain of sand to the sites at locations (x+1, y-1), (x+1, y) and (x+1, y+1); a(n) gives the number of nonempty sites after stabilization of a configuration starting with n grains at the origin. 2
 0, 1, 1, 3, 4, 4, 3, 4, 4, 7, 8, 8, 10, 11, 11, 10, 11, 11, 14, 15, 15, 17, 18, 18, 17, 18, 18, 21, 22, 22, 24, 25, 25, 24, 25, 25, 27, 28, 28, 30, 31, 31, 30, 31, 31, 36, 37, 37, 39, 40, 40, 39, 40, 40, 39, 40, 40, 42, 43, 43, 42, 43, 43, 45, 46, 46, 48, 49 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Sites containing 0, 1 or 2 grains are stable. After stabilization, there are: - 2*a(n) - n sites with one grain, - n - a(n) sites with two grains. LINKS Rémy Sigrist, Table of n, a(n) for n = 0..10000 Rémy Sigrist, Representation of the configuration for n = 100000 (blue pixels correspond to sites with one grain, red pixels to sites with two grains) FORMULA a(3*n) + 1 = a(3*n + 1) = a(3*n + 2). EXAMPLE For n = 10 : - the model evolves (for example) as follows: 1 1 3 . 2 . 2 1 10 -> 1 3 -> 1 . 3 -> 1 . . 1 3 . 2 . 2 1 1 1 - there are 8 nonempty sites in the stabilized configuration, - so a(10) = 8. PROG (PARI) a(n) = { my (s=[n], v=0); for (k=-1, oo, if (vecmax(s)==0, return (v), v += sum(k=1, #s, s[k]%3>0); s \= 3; s = concat([ s , [0], [0]]) + concat([[0], s , [0]]) + concat([[0], [0], s ]); while (#s>2 && s[1]==0, s = s[2..#s-1]))) } CROSSREFS Cf. A349990, A351783, A352226. Sequence in context: A306477 A276865 A253718 * A295570 A035004 A222290 Adjacent sequences: A350185 A350186 A350187 * A350189 A350190 A350191 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 09 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 30 17:31 EDT 2024. Contains 372971 sequences. (Running on oeis4.)