A329871 Number of static n X n placements of water source-blocks in Minecraft.

1, 2, 10, 55, 754, 18853, 82931, 70143802, 11087020614, 3243227117597, 1772826333285009, 1806938280429412270, 3430002591378184399879, 12137184871791092506807847, 80047171080361800628780500638, 983838070049011459232146327319193

Offset

0,2

Comments

In Minecraft worlds, a source block of water can be reacted with another source block, two blocks away, linearly or diagonally. This reaction creates a third "infinite" source block in the unoccupied intermediate block or blocks, so called because if the intermediate water source is destroyed or picked up by a player using a bucket, it will immediately regenerate itself.

A placement of water at several positions in an n X n board is said to be static if no infinite water sources are created that are not already present. In particular, the total quantity of water in the system is held constant.

Links

Table of n, a(n) for n=0..15.

EthosLab, Minecraft - Tutorial: Water

Gus Wiseman, The a(3) = 55 static placements of water source-blocks (black = water).

Christopher Cormier, C# Program

Mathematica

vdist[v_, w_]:=Total[Abs[v-w]];
flowdown[prs_]:=Union[prs, With[{ovs=Select[Subsets[prs, {2}], vdist@@#==2&]}, Union@@Function[{v, w}, Select[Tuples[{Range[Min@@Union[First/@prs], Max@@Union[First/@prs]], Range[Min@@Union[Last/@prs], Max@@Union[Last/@prs]]}], vdist[v, #]==1&&vdist[w, #]==1&]]@@@ovs]];
Table[Length[Select[Subsets[Tuples[Range[n], 2]], flowdown[#]==#&]], {n, 0, 3}]

Crossrefs

Dominates A273461.

The one-dimensional case is A005251.

Cf. A002416, A006498, A027624, A114901.

Sequence in context: A216721 A122826 A320129 * A108490 A323935 A370195

Adjacent sequences: A329868 A329869 A329870 * A329872 A329873 A329874

Keyword

nonn

Author

Gus Wiseman, Nov 26 2019

Extensions

a(5)-a(6) from Christopher Cormier, Dec 10 2019

a(7)-a(15) from Christopher Cormier, Dec 19 2019

Status

approved