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 A259013 a(n) is the smallest number of grains of sand placed at the center square of a (2n-1) X (2n-1) table so that some grains drop off the table by the end of the diffusion process. 7
 4, 16, 44, 88, 144, 208, 320, 408, 512, 672, 788, 948, 1096, 1288, 1552, 1768, 1960, 2208, 2456, 2708, 3028, 3384, 3648, 3964, 4348, 4728, 5076, 5448, 5884, 6308, 6708, 7176, 7644, 8240, 8664, 9132, 9764, 10276, 10816, 11404, 11992, 12516, 13264, 13816, 14388 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The diffusion rule is that if a square has more than 3 grains of sand then it loses 4 grains and each neighbor's number of grains increases by one. Initially the center square has a(n) sand grains and all other squares are empty. The final distribution of sand grains and the number a(n) do not depend on the order of the diffusion process. For this reason, it is called an "abelian sandpile model". LINKS Scott R. Shannon, Table of n, a(n) for n = 1..1000 Wikipedia. Abelian Sandpile Model PROG (MATLAB) % S(k) gives the minimum number of grains of sand needed at the center % of a (2n-1) X (2n-1) square table for some grains to drop off % the table in an "abelian sandpile model". firstsand=zeros(1, 49); S=zeros(1, 49); n=50; lim=2*n-1; A=zeros(lim, lim); for j=1:17128; A(n, n)= A(n, n)+1; while max(max(A))>=4 for xi=1:lim for yi=1:lim if A(xi, yi) >= 4 A(xi, yi)= A(xi, yi) - 4; A(xi+1, yi)=A(xi+1, yi) + 1; A(xi, yi+1)=A(xi, yi+1) + 1; A(xi-1, yi)=A(xi-1, yi) + 1; A(xi, yi-1)=A(xi, yi-1) + 1; end end end end for k=1:n-1 if A(n, n+k)==1 && firstsand(k)==0 firstsand(k)=1; S(k)=j; end end end CROSSREFS Sequence in context: A183536 A320100 A161142 * A212960 A217873 A289086 Adjacent sequences: A259010 A259011 A259012 * A259014 A259015 A259016 KEYWORD nonn AUTHOR Sezai ATA, Jun 16 2015 EXTENSIONS a(21)-a(45) from Giovanni Resta, Jun 17 2015 STATUS approved

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Last modified April 20 02:49 EDT 2024. Contains 371798 sequences. (Running on oeis4.)