login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
KEYWORD
nonn
AUTHOR
Sezai ATA, Jun 16 2015
EXTENSIONS
a(21)-a(45) from Giovanni Resta, Jun 17 2015
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.

License Agreements, Terms of Use, Privacy Policy. .

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