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

2, 3, 1, 7, 7, 8, 11, 5, 71, 3, 26, 9, 679, 77, 52, 41, 13, 769, 281, 17753, 29, 97, 47, 3713, 4271, 726433, 434657, 272, 153, 17, 8449, 2245, 33507, 167089, 46069729, 901, 362, 123, 81767, 8569, 24852386, 265721, 8118481057, 190818387, 73124, 571, 89, 93127, 18061, 20721019, 4213133, 4974089647, 1031151241, 1234496016491, 89893

Offset: 1

Author

N. J. A. Sloane, Mar 15 2015

Keywords

• nonn
• tabl

Examples

			Triangle begins:
[2]
[3, 1]
[7, 7, 8]
[11, 5, 71, 3]
[26, 9, 679, 77, 52]
[41, 13, 769, 281, 17753, 29]
[97, 47, 3713, 4271, 726433, 434657, 272]
[153, 17, 8449, 2245, 33507, 167089, 46069729, 901]
[362, 123, 81767, 8569, 24852386, 265721, 8118481057, 190818387, 73124]
[571, 89, 93127, 18061, 20721019, 4213133, 4974089647, 1031151241, 1234496016491, 89893]
...
		

Links

• Laura Florescu, Daniela Morar, David Perkinson, Nicholas Salter and Tianyuan Xu, Sandpiles and Dominos, Electronic Journal of Combinatorics, Volume 22(1), 2015.
• David Perkinson, Lecture 15: Sandpiles, PCMI 2008 Undergraduate Summer School.

Crossrefs

Main diagonal gives A256046, A256043, and A256047.

Cf. A005246, A195549, A348566.

Formula

From Andrey Zabolotskiy, Oct 22 2021: (Start)

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

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).

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

Extensions

Column 1 added by Andrey Zabolotskiy, Oct 22 2021