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

1,1

Links

Table of n, a(n) for n=1..55.

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.

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)

Example

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]
...

Crossrefs

Main diagonal gives A256046, A256043, and A256047.

Cf. A005246, A195549, A348566.

Sequence in context: A085588 A377345 A118008 * A173459 A354839 A121637

Adjacent sequences: A256042 A256043 A256044 * A256046 A256047 A256048

Keyword

nonn,tabl

Author

N. J. A. Sloane, Mar 15 2015

Extensions

Column 1 added by Andrey Zabolotskiy, Oct 22 2021

Status

approved