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A256045 Triangle read by rows: order of all-2s configuration on the n X k sandpile grid graph.

%I A256045 #27 Sep 26 2024 23:38:50
%S A256045 2,3,1,7,7,8,11,5,71,3,26,9,679,77,52,41,13,769,281,17753,29,97,47,
%T A256045 3713,4271,726433,434657,272,153,17,8449,2245,33507,167089,46069729,
%U A256045 901,362,123,81767,8569,24852386,265721,8118481057,190818387,73124,571,89,93127,18061,20721019,4213133,4974089647,1031151241,1234496016491,89893
%N A256045 Triangle read by rows: order of all-2s configuration on the n X k sandpile grid graph.
%H A256045 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 A256045 David Perkinson, <a href="https://people.reed.edu/~davidp/pcmi/lectures/15combined.pdf">Lecture 15: Sandpiles</a>, PCMI 2008 Undergraduate Summer School.
%F A256045 From _Andrey Zabolotskiy_, Oct 22 2021: (Start)
%F A256045 It seems that T(k, 1) = A005246(k+2).
%F A256045 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 A256045 T(n, k) divides A348566(n, k). (End)
%e A256045 Triangle begins:
%e A256045 [2]
%e A256045 [3, 1]
%e A256045 [7, 7, 8]
%e A256045 [11, 5, 71, 3]
%e A256045 [26, 9, 679, 77, 52]
%e A256045 [41, 13, 769, 281, 17753, 29]
%e A256045 [97, 47, 3713, 4271, 726433, 434657, 272]
%e A256045 [153, 17, 8449, 2245, 33507, 167089, 46069729, 901]
%e A256045 [362, 123, 81767, 8569, 24852386, 265721, 8118481057, 190818387, 73124]
%e A256045 [571, 89, 93127, 18061, 20721019, 4213133, 4974089647, 1031151241, 1234496016491, 89893]
%e A256045 ...
%Y A256045 Main diagonal gives A256046, A256043, and A256047.
%Y A256045 Cf. A005246, A195549, A348566.
%K A256045 nonn,tabl
%O A256045 1,1
%A A256045 _N. J. A. Sloane_, Mar 15 2015
%E A256045 Column 1 added by _Andrey Zabolotskiy_, Oct 22 2021