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Triangle read by rows: order of all-2s configuration on the n X k sandpile grid graph.
6

%I #27 Sep 26 2024 23:38:50

%S 2,3,1,7,7,8,11,5,71,3,26,9,679,77,52,41,13,769,281,17753,29,97,47,

%T 3713,4271,726433,434657,272,153,17,8449,2245,33507,167089,46069729,

%U 901,362,123,81767,8569,24852386,265721,8118481057,190818387,73124,571,89,93127,18061,20721019,4213133,4974089647,1031151241,1234496016491,89893

%N Triangle read by rows: order of all-2s configuration on the n X k sandpile grid graph.

%H Laura Florescu, Daniela Morar, David Perkinson, Nicholas Salter and Tianyuan Xu, <a href="https://doi.org/10.37236/4472">Sandpiles and Dominos</a>, Electronic Journal of Combinatorics, Volume 22(1), 2015.

%H David Perkinson, <a href="https://people.reed.edu/~davidp/pcmi/lectures/15combined.pdf">Lecture 15: Sandpiles</a>, PCMI 2008 Undergraduate Summer School.

%F From _Andrey Zabolotskiy_, Oct 22 2021: (Start)

%F It seems that T(k, 1) = A005246(k+2).

%F For the formula for T(k, 2), see the last theorem of Morar and Perkinson in Perkinson's slides. In particular, T(2*k, 2) = A195549(k).

%F T(n, k) divides A348566(n, k). (End)

%e Triangle begins:

%e [2]

%e [3, 1]

%e [7, 7, 8]

%e [11, 5, 71, 3]

%e [26, 9, 679, 77, 52]

%e [41, 13, 769, 281, 17753, 29]

%e [97, 47, 3713, 4271, 726433, 434657, 272]

%e [153, 17, 8449, 2245, 33507, 167089, 46069729, 901]

%e [362, 123, 81767, 8569, 24852386, 265721, 8118481057, 190818387, 73124]

%e [571, 89, 93127, 18061, 20721019, 4213133, 4974089647, 1031151241, 1234496016491, 89893]

%e ...

%Y Main diagonal gives A256046, A256043, and A256047.

%Y Cf. A005246, A195549, A348566.

%K nonn,tabl

%O 1,1

%A _N. J. A. Sloane_, Mar 15 2015

%E Column 1 added by _Andrey Zabolotskiy_, Oct 22 2021