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A293452 Triangle T(n,k) read by rows: T(n,k) is the number of iterations to reach a final state for an n X k lattice of sandpiles on a torus according to rules specified in A249872. 1

%I #19 Mar 11 2022 07:46:34

%S 0,1,7,2,14,28,7,35,65,133,10,47,86,198,316,22,86,134,331,487,913,28,

%T 106,164,399,696,1099,1360,50,159,288,589,930,1518,1798,2987,60,187,

%U 336,681,1070,1966,2320,3432,4340,95,265,515,1052,1386,2430,3475,4484,5977,7495,110,303,584,1184,1556,2718

%N Triangle T(n,k) read by rows: T(n,k) is the number of iterations to reach a final state for an n X k lattice of sandpiles on a torus according to rules specified in A249872.

%H Joerg Arndt, <a href="/A293452/b293452.txt">Table of n, a(n) for n = 1..5050</a> (rows 1..50)

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Abelian_sandpile_model">Abelian sandpile model</a>

%F T(n,n) = A249872(n).

%F Conjecture: T(n,1) = A023855(n).

%e Triangle begins:

%e 0

%e 1, 7

%e 2, 14, 28

%e 7, 35, 65, 133

%e 10, 47, 86, 198, 316

%e 22, 86, 134, 331, 487, 913

%e 28, 106, 164, 399, 696, 1099, 1360

%e 50, 159, 288, 589, 930, 1518, 1798, 2987

%e 60, 187, 336, 681, 1070, 1966, 2320, 3432, 4340

%e 95, 265, 515, 1052, 1386, 2430, 3475, 4484, 5977, 7495

%e ...

%Y Cf. A249872.

%K nonn,tabl

%O 1,3

%A _Joerg Arndt_, Oct 09 2017

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Last modified April 19 09:23 EDT 2024. Contains 371782 sequences. (Running on oeis4.)